Not sure exactly what sorts of problems you are having with these cats (or stray dogs) but some of the minor ones can be solved with a large dose of cayenne pepper.
If you have either a dog or cat that is using your flowerbed or your front yard for a potty, you can discourage it by picking up the mess, and then sprinkle the spot with a good dose of cayenne pepper.
A dog or cat will use the scent of their last leavings to find the spot they last went. So if you want to train you own dog to go to the same place in your own yard (or your neighbors, hehehehe), pick the mess, put in the spot you want them to go and they will find it. Do this every time they make a mess where you don’t want it. Within a very short time you will have it trained.
If you just want to get rid of the animal, clean up the mess, leave the pepper, generously, (repeat after a rain) and the animal will not be around for long.
If you are training your own dog, don’t use as much pepper. As for harming the animal, never heard of it doing so beyond the temporary effect. But I am sure some bleeding heart animal lover will tell you this is cruelty.
I have used this on a couple of my pets and never had any long-term problems.
I have used it on my neighbor’s pets too. Works great. One was a digger, kept digging under my fence. I put the pepper in the hole. About an hour later I heard the dog yelping like a scaled dog. But he never touched that hole again. He moved down the fence line, and it treated that hole too. Same effect. To this day, I have never even seen him even close to the entire fence line. Problem solved. Dog still loves me when I go over for BBQ’s. Neighbor never knew a thing.
It works on opossum, skunks and other varmints.