Hi. My 10 year old cat began today acting strange and unwell. He was not wanting to go out, lethargic, and has half open eyes. Then he began walking in counter-clockwise circles with some unstability in his back legs. I don't know what to do.

There a number of things that may be going on with your cat.
Only your Vet can tell you for certain.
But a couple of things that come to mind are vestibular disease (similar to vertigo in humans) left untreated it will NOT get better.
Could it be that he has gotten into something toxic?
A tumor of some sort.
My suggestion would be to get him to the Vet pronto.
Best wishes