Opossum are really docile most of the time (and eat ticks and other bugs you don't want!) I agree with getting a live box trap, they love cat food, I wonder if that is what it went into the basement for?
Call the wildlife center and see if they can give you a trap or come and get the opossum for you. Let them know about the cat also.
You will probably have to catch & release yourself or pay a service to it for you
If you're in Dublin or UA, for sure call SCRAM. They are a service of Ohio Wildlife Center. Dublin and UA have contracts with SCRAM for reduced rates.
The cat is more of a local shelter/animal control thing
You need to trap the opossum. Then you can release it away from your home. If you are afraid to trap it you will need to call someone out to trap it for you.
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