Your post didn't indicate what was the birth date of your Great Grandfather. Hopefully it was on the WWI Draft Registration you found (or was it WWII?). Where did they settle after first arriving? What are the possible years that they did arrive?
I found on a manifest that this person's destination was Athens, Ohio:
Name: Ivar Paananen
Arrival Date: 9 Sep 1905
Birth Year: abt 1884
Port of Departure: Southampton
Port of Arrival: New York, New York
Ship Name: St Louis
I'm not saying that is your G-Grandfather. I found it by just working with the surname. And, the surname may not even be correct.
Here are some resources for your search:
Finnish Heritage Museum of Fairport Harbor http://finnishheritagemuseum.org/
Emigration from Finlandhttp://sydaby.eget.net/swe/emi_ref.htm