If someone paid for some house repairs on their credit cards am I responsible for paying those bills

You have a contract with your roommate; your question doesn't indicate whether it was in writing. If you can prove the terms of the contract are as you say they are, you won't have to pay the bills, if you can't, you might be held liable. Proving that you paid all of the house bills does not necessarily prove that the improvements were your roommates responsibility. The court might interpret your agreement as one involving real estate, which must be in writing in every state that I can think of. You may have a tough go here. Stick with the "none of the expenses are in my name argument", but contact an Ohio attorney who specializes in real estate leases and agreements. Obviously, you have a lot at stake. Good luck.