I moved to Wisconsin before applying to school to establish residency. I can't speak for Ohio, but Wisco requires that you live in the state, working full time, pay state taxes (obviously), have a state drivers license & license plates, and register as a Wisconsin voter all for 12 full months to gain residency. there are ways around the 12 month rule, like buying a house. I am SOOO glad I established residency before applying and would do it again in a heartbeat. I also did not want to attend my IS school (USU/WSU) and there is no chance I would have ever been accepted to UW as an OOS.
I don't know if this is true, but I read somewhere on one of these threads that some schools like IS students who are from different states? Maybe because of the diversity aspect?
Anyway, it worked for me in Wisconsin. But be sure to talk to the school and make sure you complete all the little things (like registering to vote) to be considered a resident in time for the application cycle. I would suggest getting a copy of the form (from the school) that they have you fill out when you apply to become a state resident. It will be a good check list for you.