Do you have Habitat for CAts in your area? the catch them, neuter them and return them. It really make the cat's lived happier.
I had them pick up my strays a few years ago - they got my 3 at the time, and one other who used to just walk by the house every day. When they brought them all back, that poor little guy would still walk by every day, but he would cross the street one house before mine and come back over one house past! Poor guy!!! Must have thought I was some kind of monster.
I have 4 right now - all homeless at one time. No problems with any of them.
Never leave food out. It attracts other unwanted animals that you don't want around.