In my opinion, those are goats. In any case, definitely not
moose or elk. As someone else stated, from their condition I would also venture that they've either escaped from or been purposely released by someone. Not only are goats BIG-TIME efficient escape artists, but many people have been known to get into them, change their minds, & leave them to fend for themselves. Sad but true. Although I don't have the time to go through every breed on the following list, you may find something on this extremely thorough & well-photographed site that resembles your "wild" Ohio herd. You'll also see that this site states that unlike sheep (domesticated, not wild-breed sheep), escaped domesticated goats are more likely to survive as ferals. Enjoy!