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I'm sorry to hear about your situation. You're correct that Ohio is an at-will state. At-will employment means that without a contract, you have no contractual or other right to employment with the company. The company is entitled to fire you for any reason: a good reason, a poor reason, or no reason at all--as long as the company does not fire you for an illegal reason (race, gender, age, religion, etc...). But it extends beyond firing, to hiring, promotions
, demotions, wage
cuts and raises, disciplinary actions
, and even scheduling. Unless you can show that this was done in violation of a contract, union agreement, or a clear violation of an unambiguous and binding clause against the employer, or that it was done because of some minority status (age, race, gender, religion, disability) that you have, then they do have this discretion.
In short, unless you have a basis that avoids the at will
relationship (such as a contract that says that they can't terminate you but for "good cause", etc...) then I'm afraid to say that you wouldn't have a case to sue them (as illogical their rationale was and as incompetent the "investigation" that implicated you).
Now you should still be able to qualify for unemployment, as the reasons given do not indicate that you shouldn't. Unemployment is available to individuals who are unemployed due to no fault of their own. It seems to be the employer's decision and overzealousness in enforcing rules. It does not appear to be misconduct to a level that would make you ineligible for unemployment. Now if you do apply and they deny it, don't be surprised, as this is often the case at the first level. You usually need to file an appeal to get your side of the case heard.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!