Why did Europeans emigrate to America?
One word. Land. In the US, one had the possibility of owning land (remember the Homestead Act), which in Europe was not much of a possibility for those outside of the rich or noble classes. Poverty in Europe and the promise of oppurtunity in America was also another reason. The over-population also contributed. Besides in the US there was also the chance to know religious and political freedom like no where else. For the Irish, the potato famine was a major cause. For Black Sea-Germans, the Russian nationalism in czarist Ukraine put pressure on them to leave (late 1800's early 1900's). Wars in Europe. There are all sorts of reasons.
Where did the Jewish immigrants in Europe came from?
First, you need to define what you mean when you say "Jews". There are at least two ways to define a Jew, by heritage or by religion. Not all people descending from the original tribes of Israel chose to remain adherents of Judaism. Not all people who worship in sinagogues descend from the original tribes of Israel. Around 1000, Judaism was a full-blown world religion, with native (rather than descending from the original tribes of Israel) followers spread from Ethiopia to Crimea and from Spain to Khazaria. The last Ethiopian Jews (about 20,000 of them) were airlifted to Israel in 1980s. Small Karaite populations still exist in Ukraine and Lithuania.
Where did German Jews try to migrate to find safety from the Nazi terror?
German Jews, or Jews of occupied German Terriories tried to get the Western Europe of the Americas for safety. However many of the allied nations that could have helped save them turned many away. Typically many tried to get to Sweden, because it was a short jump across the channel the separated Denmark from Sweden. Several Jews were forced to live in portions of Polish cities called Ghetto's. These areas of the cities were very dirty and severally run down. Many times the Germans would force thousands of Jew to live in these Ghettos, however they would only be able to handle a fraction of thise number, so they were severly overcrowded. The most famous one was the Ghetto in Warsaw. Many time the Jews would try to revolt against the Germans only to have it crushed. Life here was terrible and typically it was only a matter of time till the Jews were shipped to Concentration or Death Camps.