I mostly don´t have strays, but pets of other households. They wander in (no one has to invite them in), stay for a while and leave again. Or not. I think, they glitch, because they just don´t leave and seem to be pretty content at the house, but when I restart the game, they are gone. I could probably reset them but as long as they don´t have fleas, I let my sims have fun with them.
https://i.postimg.cc/Cx4QyJRw/Screenshot-x6807.jpg
This kitten was wildly popular.
https://i.postimg.cc/zv1CGZQ6/Screenshot-x3344.jpg
Also, sometimes there are random horses in the living room. This one just ran through the wall.
https://i.postimg.cc/59w5kyYV/Screenshot-x3508.jpg
And this deer, which really didn´t like my sim. It poofed away after this. Bit creepy.