Basically what it says on in the title. What are the effects on the German tribes east of the Elbe river if the Roman Empire manages to conquer the lands between the Rhine and the Elbe?
It really depends on the style of government which takes hold. Its conceivable that the Romans get to the Elbe, but why? Everything the could gain from Germany was already found within the Empire. While Gaul was at least quasi urbanized Germany might as well be Siberia. The land is terrible for agriculture without The heavy plow and unless that advancement can be sped up several hundred years Germany is nearly worthless and the Rhine will seem a much better alternative to the Emperors who follow after the conquest.
With that in mind, you will see several forts and trading cities established and begin the framework of Roman order. After a generation locals will have had time to adjust and see the benefits of Rome just in time for a usurping general from the region pull his legions to seize the throne. Germany will be abandoned much like Britain. However with a rump roman-german state, even a weak one, the migrations will occur much differently.