Are they usurpers who immigrated from other parts of the world to take over Palestine?
According to Wikipedia, the History of the Jews in the Land of Israel begins with the ancient Israelites (also known as Hebrews), who settled in the land of Israel. The Israelites traced their common lineage to the biblical patriarch Abraham through Isaac and Jacob. Jewish tradition holds that the Israelites were the descendants of Jacob's twelve sons (one of which was named Judah), who settled in Egypt. Their direct descendants respectively divided into twelve tribes, who were enslaved under the rule of an Egyptian pharaoh. In the Jewish faith, the emigration of the Israelites from Egypt to Canaan (the Exodus), led by the prophet Moses, marks the formation of the Israelites as a people.
Throughout the centuries, in spite of oppression, banishment, and slaughter, there was an uninterrupted continuity of Jewish life in the country. The Jewish community in the land of Israel has always played a unique role in Jewish history.
Violence and discrimination against Jews in Arab countries began many years before 1948 and escalated after 1948 despite the fact that most Jewish residents were indigenous and for the most part held Arab citizenship. Sometimes the discrimination was state sanctioned, other times it was the result of anti-Jewish harassment by non-Jews. Regardless of its source, harassment, persecution and the confiscation of property took place.
The first migrations to Palestine began long before the state of Israel was formed in 1948. The first Aliyah to Ottoman Palestine began in the 1800's http://en.wikipedia.org/wiki/First_Aliyah
Wikipedia tells readers the Jewish exodus from Arab lands refers to the 20th century expulsion or mass departure of Jews, primarily of Sephardi and Mizrahi background, from Arab and Islamic countries. The migration started in the late 19th century, but accelerated after the 1948 Arab-Israeli War. According to official Arab statistics, 856,000 Jews left their homes in Arab countries from 1948 until the early 1970s. Some 600,000 resettled in Israel. Their descendants, and those of Iranian and Turkish Jews, now number 3.06 million of Israel's 5.4 to 5.8 million Jewish citizens.  The World Organization of Jews from Arab Countries (WOJAC) estimates that Jewish property in Arab countries would be valued today at more than $300 billion and Jewish-owned real-estate left behind in Arab lands at 100,000 square kilometers (four times the size of the State of Israel). 
The great majority of Jews in Arab lands eventually emigrated to the modern State of Israel. Activist groups such as JJAC and JIMENA claim that there was a collusion among Arab states to persecute Jews as part of their struggle against Israel.
The process grew apace as Arab nations under French, British and Italian colonial rule or protection gained independence. Further, anti-Jewish sentiment within the Arab-majority states was exacerbated by the Arab-Israeli wars. Within a few years after the Six Day War (1967) there were only remnants of Jewish communities left in most Arab lands. Jews in Arab lands were reduced from more than 800,000 in 1948 to perhaps 16,000 in 1991.
Some claim that the Jewish exodus from Arab lands is a historical parallel to the Palestinian exodus during the 1948 Arab-Israeli War, while others reject this comparison as simplistic.[6
Arab Nations - In 1945, there were between 758,000 and 866,000 Jews (see table below) living in communities throughout the Arab world. Today, there are fewer than 7,000. In some Arab states, such as Libya (which was once around 3% Jewish), the Jewish community no longer exists; in other Arab countries, only a few hundred Jews remain. http://en.wikipedia.org/wiki/Jewish_exodus_from_Arab_lands
Iran - At the time of the establishment of the state of Israel in 1948, there were approximately 140,000–150,000 Jews living in Iran, the historical center of Persian Jewry. Over 85% have since migrated to either Israel or the United States, with the migration accelerating after the 1979 Islamic Revolution, when the population dropped from 100,000 to about 40,000. On March 16, 1979, Habib Elghanian, the honorary leader of the Jewish community, was arrested on charges of "corruption", "contacts with Israel and Zionism", "friendship with the enemies of God", "warring with God and his emissaries", and "economic imperialism". He was tried by an Islamic revolutionary tribunal, sentenced to death, and executed on May 8, one of 17 Iranian Jews executed as spies since the revolution.
Estimates of the Jewish population in Iran vary. In mid- and late 1980s, it was estimated at 20,000–30,000, rising to around 35,000 in mid-1990s, and estimated at less than 40,000 nowadays, with around 25,000 residing in Tehran. However, Iran's Jewish community still remains the largest in the Middle East outside of Israel.  http://en.wikipedia.org/wiki/Iranian_Jews
Iraq - In the 1930s, the situation of the Jews in Iraq deteriorated. Previously, the growing Iraqi Arab nationalist sentiment included Iraqi Jews as fellow Arabs, but these views changed with the introduction of Nazi propaganda and the ongoing conflict in the Palestinian Mandate. Despite protestations of their loyalty to Iraq, Iraqi Jews were increasingly subject to discrimination and harsh laws. On August 27, 1934 many Jews were dismissed from public service, and quotas were set up in colleges and universities. Zionist activities were banned, as was the teaching of Jewish history and Hebrew in Jewish schools. Following Rashid Ali's pro-Axis coup, the Farhud ("violent dispossession") pogrom of June 1 and 2, 1941, broke out in Baghdad in which approximately 200 Jews were murdered (some sources put the number higher), and up to 2,000 injured -- damages to property were estimated at $3 million. There was also looting in many other cities at around the same time. Afterwards, Zionist emissaries from Palestine were sent to teach Iraqi Jews self-defense, which they were eager to learn. ." (Simon, Reguer, and Laskier, p 364)
In 1948, the country was placed under martial law, and the penalties for Zionism were increased. Courts martial were used to intimidate wealthy Jews were detained, Jews were again dismissed from civil service, quotas were placed on university positions, and Shafiq Ades (one of the most important anti-Zionist Jewish businessmen in the country) was arrested and executed for allegedly selling goods to Israel, shocking the community (Tripp, 123). Additionally, like most Arab League states, Iraq forbade any legal emigration of its Jews on the grounds that they might go to Israel and could strengthen that state. However, intense diplomatic pressure brought about a change of mind. At the same time, increasing government oppression of the Jews fueled by anti-Israeli sentiment, together with public expressions of anti-semitism, created an atmosphere of fear and uncertainty.
By 1949, the Iraqi Zionist underground had become well-established (despite many arrests), and they were smuggling Iraqi Jews out of the country illegally at a rate of 1,000 a month (Simon, Reguer, and Laskier, p 365). Hoping to stem the flow of assets from the country, in March 1950 Iraq passed a law of one year duration allowing Jews to emigrate on condition of relinquishing their Iraqi citizenship. They were motivated, according to Ian Black, by "economic considerations, chief of which was that almost all the property of departing Jews reverted to the state treasury" and also that "Jews were seen as a restive and potentially troublesome minority that the country was best rid of." (p.91) Israel was initially reluctant to absorb so many immigrants, (Hillel, 1987) but eventually mounted an airlift operation in March of 1951 called "Ezra and Nehemiah" to bring as many of the Iraqi Jews as possible to Israel, and sent agents to Iraq to urge the Jews to register for immigration as soon as possible.
From the start of the emigration law in March 1950 until the end of the year, 60,000 Jews registered to leave Iraq. In addition to continuing arrests and the dismissal of Jews from their jobs, this exodus was encouraged by a series of bombings starting in April 1950 that resulted in a number of injuries and a few deaths. Two months before the expiry of the law, by which time about 85,000 Jews had registered, another bomb at the Masuda Shemtov synagogue killed 3 or 5 Jews and injured many others. The law expired in March 1951 but was later extended after the Iraqi government froze the assets of departing Jews, including those who had already left. During the next few months, all but a few thousand of the remaining Jews registered for emigration, spurred on by a sequence of further bombings that caused few casualties but had great psychological impact. In Operation Ezra and Nehemiah, some 120,000 Jews were airlifted to Israel via Iran and Cyprus. http://en.wikipedia.org/wiki/Iraqi_Jews
Jordan - Following the United Nations Partition Plan for Palestine of 1947, Jordan was one of the Arab countries that attacked the new Jewish state of Israel. It gained control of the West Bank, and expelled its remaining Jewish population. Jordan lost the West Bank during the 1967 Six-Day war, but did not relinquish its claim to the West Bank until 1988. Jordan did not join Syria and Egypt in attacking Israel during the 1973 Yom Kippur War. Jordan eventually signed the Israel-Jordan Treaty of Peace in 1994, normalizing relations between the two countries. http://en.wikipedia.org/wiki/Jordanian_Jews
Libya - By 1967, the Jewish population of Libya was down to 7,000. After the Six-Day War between Israel and its Arabic neighbours more revolts by the Libyan population led to another series of attacks on Jews. During these attacks 18 people were killed and more were injured.  Leaders of the Jewish community then asked King Idris I to allow the entire Jewish population to "temporarily" leave the country; he consented, even urging them to leave. The Italian navy supplied an airlift and the aid of several ships to help evacuate more than 6,000 Jews to Rome in one month; the evacuees were forced to leave their homes, their businesses and most of their possession behind. Of these 6,000 more than 4,000 soon left Italy for Israel or the United States. The ones who remained built up a Jewish community in Rome, which now consists of 15,000 people including many from Libya and their descendants, which have a large influence on the community. [6
Saudi Arabia - During the Gulf War (1990-1991), when approximately a half million US military personal assembled in Saudi Arabia, and many were then stationed there, there were many Jewish US service personnel in Saudi Arabia. It is reported that the Saudi government insisted that Jewish religious services not be held on their soil but that Jewish soldiers be flown to nearby US warships.
Syria - Syrian Jews derive their origin from two groups: those who inhabited Syria from early times and the Sephardim who fled to Syria after the expulsion of the Jews from Spain (1492 C.E). There were large communities in Aleppo, Damascus, and Beirut for centuries. In the early twentieth century a large percentage of Syrian Jews emigrated to the U.S., Central and South America and Israel. Today only a few Jews still live in Syria. The largest Syrian-Jewish community is located in Brooklyn, New York, and estimated at 40,000.
In 1944, after Syria gained independence from France, the new government prohibited Jewish immigration to Palestine, and severely restricted the teaching of Hebrew in Jewish schools. Attacks against Jews escalated, and boycotts were called against their businesses.
When partition was declared in 1947, Arab mobs in Aleppo devastated the 2,500-year-old Jewish community. Scores of Jews were killed and more than 200 homes, shops and synagogues were destroyed. Thousands of Jews illegally fled Syria to go to Israel. http://en.wikipedia.org/wiki/Jews_of_SyriaPoland - Dariusz Stola of the Institute of Political Studies, Polish Academy of Sciences, called the events that followed in 1967 and 1968 as an anti-Semitic "massive hate campaign," clearly aimed at Polish Jews, despite the use of the word Zionists:
The term “anti-Zionist campaign” is misleading in two ways, since the campaign began as an anti-Israeli policy but quickly turned into an anti-Jewish campaign, and this evident anti-Jewish character remained its distinctive feature. Firstly, the words Zionism and Zionist, were a substitute and code-name for “Jew” and “Jewish.” Secondly, “Zionist” signified Jew even if the person called Zionist was not Jewish. PDF
More intense official government persecution followed, in the words of The YIVO Encyclopedia of Jews in Eastern Europe (Yale University Press): "The Interior Ministry compiled a card index of all Polish citizens of Jewish origin, even those who had been detached from organized Jewish life for generations. Jews were removed from jobs in public service, including from teaching positions in schools and universities. Pressure was placed upon them to leave the country by bureaucratic actions aimed at undermining their sources of livelihood and sometimes even by physical brutality."(PDF) http://en.wikipedia.org/wiki/1968_Polish_political_crisis
Russia - The vast territories of the Russian Empire at one time hosted the largest Jewish population in the world. Within these territories the Jewish community flourished and developed many of modern Judaism's most distinctive theological and cultural traditions, while also facing periods of intense antisemitic discriminatory policies and persecutions. In the late 1980s and early 1990s, many Soviet Jews took advantage of liberalized emigration policies, with over half their population leaving, most for Israel, the United States and Germany. Despite this, the Jews in Russia and the nations of the former Soviet Union still constitute one of the larger Jewish populations in Europe. http://en.wikipedia.org/wiki/Aliyah_from_the_Soviet_Union_in_the_1970s
Egypt - Egyptian Jews constitute perhaps the oldest Jewish community outside Israel in the world. While no exact census exists, the Jewish population of Egypt was estimated at fewer than a hundred in 2004, down from between 75,000 and 80,000 in 1922. The historic core of the indigenous community consisted mainly of Arabic-speaking Rabbanites and Karaites. After their expulsion from Spain, more Sephardi and Karaite Jews began to emigrate to Egypt, and their numbers increased with the growth of trading prospects after the opening of the Suez Canal, to constitute the commercial and cultural elite of the modern community. The Ashkenazi community, mainly confined to Cairo's Darb al-Barabira quarter, began to arrive in the aftermath of the waves of pogroms that hit Europe in the latter part of the 19th century. In the early 20th century the Jewish community, fleeing persecution in Europe, found safe haven in Egypt, but conditions worsened for Egyptian Jewry by the 1940s, and the decline accelerated after Gamal Abdel Nasser mounted a coup d'etat in 1952.
Ethiopia - By the mid-1970s, a severe mass hunger broke over Ethiopia, which got the Ethiopian government asking for help from the Western world, including Israel, and in this form the government eventually allowed the Jewish Ethiopians to immigrate to Israel.
In the absence of full diplomatic relations with Ethiopia, The Israeli Mossad contacted officials in Sudan, which is adjacent to Ethiopia. Thousands of Jews from Ethiopia traveled by foot to the border with Sudan, and waited there in temporary camps until they were flown to Israel. Between the years 1977 and 1984, these immigrants were lead from those camps to Israel by means of vessels of the Israeli Sea Corps and airplanes. Until operation Moses, about 8,000 arrived in Israel in a dangerous journey in which about 4,000 Jews, at least, perished from plagues, hunger and murderous attacks of robbers. http://en.wikipedia.org/wiki/Aliyah_from_Ethiopia
This is by no means a complete history of the immigration to Israel by Arabs, Palestinians or individuals who practice the Jewish faith. But it does shine a light on the fact that many of Israel's citizens were banished or forced to leave their country of origin by the very nations who now call for Israel's destruction.
Timeline of Jewish History: http://www.jewishhistory.com/jh.php?id=Timeline&content=Timeline
Map Image courtesy of Wikipedia (1789 map of Holy Land and the Original 12 Tribes).
Historical Documentation courtesy of Wikipedia.org