Heres some tips, we use to have wild/neighbours cats in our garden , they use to crap and throw up on our lawn, scratch our garden furniture,etc. But either theyve all been run over or i`ve scared them away with the following...
Fill up some clear plastic bottles half full of water and leave a few around the garden. it spooks the cats. It might take a while.
Drop some citrus skins and garlic around the place. Not sure if this works and anyway the ants usually cart it all off in a couple of days.
If you see the cat, grab either a bucket of water or another non-breakable object to throw at it and run after it screaming "you f**king bastards"
Failing all of that, get some razor wire around your walls and mine the perimeter.