There are a lot of kinds of auto auctions. Don't buy a salvage auto from any auctions because you might have problems insuring it and it could cause you some terrible problems. The vehicle might have been in water for a prolonged time or anything you can imagine so proceed with caution and always check to make sure it wasn't a salage vehicle before you buy it. It will say salvage on the title of the car.
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Check with your local new car sellers and ask them who buys their trade-ins and find out what auction takes them to resell.
Generally, if a trade-in is more than three years old they won't keep it on their lot. Maybe the local used car sales offices will tell you what auctions they go to fpr sale.
Watch in your local newspaper for Police Auctions. Once I brought a decent economy car with a not too bad dented fender for real cheap. It ran good. Trouble is you buy these sight unseen until the auctionday and know nothing about them. Now they do list the vehicles that will be auctioned in the paper, but you don't know the condition so it is good to take someone with you who know some about cars.
I paid three hundred dollars for the one I bought and I took a chance, but for me it was worth it.
I am not sure where Brooklyn, Ohio is. I am in VA. I know a lot of people around here go to the Stateline Auction just across the West Va line somewhere west a ways beyond Winchester, VA, Also there is a big Auto Auction just across the Penna. line toward the same northwestern direction. Maybe you could find them on the computer.
But the police auctions are listed in the local newspaper and happen about every three months. Oh, I do know that the state capital offices in VA also have miscellanious auctions with office equipment and there are also cars sold there too maybe once a year.
The Stateline Auctions are every week end.
Check Carmax too. They have some pretty good deals, but that isn't an auction.
Good luck!