Personally, I don't see that he's breaking any laws at all. He's being a jerk, yes, but that's not illegal
If killing a rooster is illegal, I'm in so much trouble. I've got the evidence right here in my freezer.
If having a bird taken by a predator is illegal, most of us on this board are busted.
If hosing a bird or dunking it in water is illegal, my Grandma would be in jail.
I think what you have is just a basic philosophical difference. You see chicken and likely all animals as pets. He doesn't, he sees them as livestock. It's just two different points of view, neither is wrong, just different. You will find both ends of the spectrum on this board, and we all try to be pretty tolerant of each other's viewpoint.
Now, his birds on your property is another story. It doesn't matter that you rent, etc. Complain to the landlord. I don't know if animal control in your area will address that or not....it seems kinda hit or miss. I don't think there are many legal ramifications on animals roaming your property except you can trap them and turn them into the shelter. But the landlord needs to enforce some boundaries on that issue.
Why do you interact with this person to the extent you do?