OC is legal in Ohio with no permit/license. As long as it is legal for you to own a gun, you can OC it. But, keep the following in mind:
As soon as you get in/on the vehicle, it is legally concealed. With no Ohio-recognized license, you will need to unload the gun, and the magazines & speed loaders. Concealed carry without a license = felony.
Without an Oh-recognized license, stay out of the bars - or any place that serves alcohol. Places that sell it are ok (e.g. the Kroger that had me arrested for an afternoon), just not if it is served. If you have an Oh-recognized license, then you are ok in bars, etc. as long as you are not drinking.
If you carry concealed and are licensed, you must notify LEOs that you interact with. If you are carrying concealed illegally, you do not have to notify LEOs.
While OC is legal, it isn't always socially acceptable. People will occasionally call the police. I strongly recommend a voice recorder. 99.99% of the time just being nice will defuse any problems.
If you see a gun-buster sign, don't go in armed. I suggest you spend your money elsewhere. There are some signs that read (paraphrased) 'we sell booze, you may be in violation of the law if you come in here armed.' Don't confuse these with no-gun signs. These signs are posted at places that have liquor licenses and have no force of law.