We had a kitten that was hanging around our house last spring. I eneded up feeding it. I also left my garage door open a little, so it had a place to stay. The cat is now bigger, it's friendly (when we pet him, he just melts) but skitish. It's getting colder in WI, and I'm not sure what to do. We can't leave our garge door open (snow). We have 2 dogs and 1 cat already. The shelters are over full, so the cat would probably be put down since it's ferrel. I called out vet and with the inital costs (with a free exam) it's about $400. They want feline lukemia test, deworm, fecal test, rabies shots, neuter/declaw. It's a tough sell for my husband. We also don't know how it will adjust being inside, we have 4 kids with lots of activity. I also don't know if the cat will go in the litter box after going outside all this time. I did put a box with litter in the garage but he didn't use it, but he had access to the outside. It's a lot of money to invest with no guarantees. Anyone ever deal with this issue, any suggestions? I just don't want the cat put down! It's not his fault.
Anyway, if you care this much for the cat, I would go ahead and get it shots, and neutering/spaying. Testing for leukemia is a must, especially since you say the cat is already hanging out in the garage. You don't want a disease such as that transferred to your cats in the house. You are kind to care for this cat. 
and a ball hanging from a string. I'd hate to leave him out in the cold and end up having something bad happen to him. Try leaving the door open a bit during the day, and if he's inside around dinnertime, just close the door and let him back out in the morning.
Well, ok once we actually got a cat from the humane society so not directly off the streets.