Question: I signed a contract with my employer stating that for any and all reasons I am not working at that company before 2 years, I have to pay back x amount of dollars for the cost of training. Now this wasn't a small sum of money, but I got fired for reasons unknown (lack of "performance"). Is this common practice (and/or legal) in Ohio or elsewhere?

Answer: 
You'd need to ask a lawyer about the legality. I have seen a lot of strange things in contracts and normally it's best to abide by them.

However once I leave a job I ignore anything the employer threatens me with. The last couple had sour grapes since many of their clients followed me out. Legal action is a costly exercise and I've never actually been prosecuted but I have been threatened twice. I wasn't sacked either time though, but I'd still ignore it if I was. This is probably your best strategy, don't answer emails, throw letters away unread, don't admit culpability for anything.

It would cost your employer quite a chunk of money (for a risk) just to get the process started against you. The longer you delay the more it costs them up front. If you're going to get prosecuted, then you're going to get prosecuted, there is no need to make it any easier or cheaper for the ex-employer and every reason to delay as long as possible.
A regular search, <https://www.google.com/?ion=1&espv=2#q=recoup+training+costs+employee+after+firing+them+ohio> might help you a little bit.  

It appears that the answer is - it depends.  

Most of the info is directed at employees who leave voluntarily. 

Did you know that a fired employee can sue for wrongful termination? I've seen employers agree to lots of things to avoid that suit. Suits cost a lot of money, especially that one. They may be willing to agree to not be sued and not sue you. This is especially true if it is a large or tiny company. 

Regardless of the wording of the question - including the legality part, it is best to get an employment attorney in the state in question.