I have not found a real cheap way to travel through Finnland. A oneway ticket with Finnish Railways from Oulu to Helsinki or v.v. costs between 66.20 € and 72 € depending on the train. You can get a 15% group discount if you are a group of at least three (!) people. Student discount is only available for those who study in Finnland.
Another option is to fly. Blue1 offers quite offen cheap domestic flights in Finnland.