I haven't really found anything about this online. Was it only Aryans that were allowed to migrate to Nazi Germany or were the borders shut completely?
Point 8 of the NSDAP 25 points says "8. Any further immigration of non-Germans must be prevented. We demand that all non-Germans who have entered Germany since August 2, 1914, shall be compelled to leave the Reich immediately." This was made before Hitler rose to power so I don't know if it was fully enacted but its likely it was.
The Nazi state imported huge numbers of workers from occupied Eastern Europe to work in manual labor occupations. The largest numbers came from Poland and Ukraine. They did not make the same wages or have the same rights as Germans in the Reich. http://web.archive.org/web/20080415124110/http://projekte.geschichte.uni-freiburg.de/herbert/uhpub/forcedlaborers.html