Snake Doctor

We have a new cat, a stray that we rescued.
We'd been feeding him for about a year, and a few weeks ago he was really banged up, head was all torn up, missing a chunk out of his ear, and his toe on his back paw was really messed up and almost gangrenous....the vet said he definitely would have gotten gangrene and probably died if we hadn't brought him to the vet when we did.

Anyways, sometimes this guy uses the litter box, and other times he doesn't. We can't figure out why.
I googled this and found a few tips, implemented all of them, and the little fucker just pissed on the carpet again....and we just steam cleaned them yesterday!!

Anyways, my patience is wearing thin and I'd really hate to put him out and see him get all banged up and shit again.....but I can't have a house that smells like cat urine.
If any of you have any suggestions that will keep this kitty from becoming homeless I'd appreciate it.

Thanks