mostly the West Bank and Gaza Strip
Many do, but the majority do not.
Substantial numbers do.
Jews and Palestinians.
it move to the strips
Yes. The Palestinian Militant group Hamas is currently in control of the Gaza Strip and the only people who live there are Palestinians.
1.82 million Palestinians live in the Gaza Strip.
The Gaza Strip
The small coastal area where 1 million Palestinians live is called the Gaza Strip. It is located on the Eastern coast of the Mediterranean Sea.
The question as posed is nonsensical. Palestine is a land and lands cannot be homeless, only people can. If the question is how long have Palestinians been homeless, the answer depends on who you consider to be a Palestinian. There are numerous Palestinians who live in Israel, the Palestinian Territories, of the Palestinian Diaspora who live in homes and have citizenship of the States in which they live. (The status of Palestinians in the Occupied Territories is a little different.) In any case, to say that these people are homeless would be, by definition, incorrect since they live in homes. There are also Palestinians who have lived their entire lives in Refugee Camps. Those Palestinians and their ancestors have lived in Refugee Camps since either 1948 or 1967, the two times the Palestinians have fled in the wake of the Israeli-Arab Wars.
we all hope that they will.
Palestinians having been living in the West Bank for the last 800 years at least, so it should not surprise us that they currently live there. Additionally, numerous Palestinians fled Israel during the Jewish-Arab Engagement in 1947-1949 and many of those Palestinians ended up in the West Bank. As a result, they began to create lives for themselves in the West Bank.
Israel controls 78% of the former Mandate of Palestine compared with 22% in the West Bank and Gaza. However, it should be noted that Palestinians are not forced to live there; they can literally live anywhere in the world other than Israel and a large number of Palestinians who did not flee Israel live inside of Israeli borders without restriction.