Did some messing around on acestry.com this morning and found a ship manifest with record of an Adam Block (same name as Gradma S's Dad). It's the manifest for the S.S. Patricia leaving Hamburg Germany on April 1, 1901. All that sounded right to me.
So if that's him, he was 34 at the time traveling with his wife Catha (27), younger brother Johanna (30) and his wife Elisabeth who's age I can't make out. They would have arrived in the port of New York and their final destination is listed as Oshkosh, Wisconsin. They were farmers. Then the part that really interested me. It says they were Russian. I admit it's hard to read some of the stuff on that form. So if you're in the mood, have a look for yourself. His name is on line 9. If you want me to email you the high-res JPEG so you can zoom in and stuff, just ask.
The closest thing I could find to the city Adam listed as his last residence is Podhájska. It's a small village in Slovokia that's been around a while. In 1901, it was in Hungary. The Hungarian ethnic assimilation policies of that time (refered to as Magyarization), may have been the reason Adam left his homeland. Though if you read the discussion on that wiki article, someone argues that economic reasons were why Hungarians emigrated at the time. Still, why isn't Hungarian listed as his nationality? Perhaps rather than Russian, the nationality he named was Rusyn. The short lived independant Rusyn state formed after WWI was Podkarpatská Rus. That also has some similarity to the last residence listed on the manifest. Though he could have been Russian.
This is all conjecture on my part of course. So help me out - let's solve this mystery. Why did Adam Block emigrate? Where in Hungary did he live? Who were his parents?