Ok, I only read the first page so forgive me if I'm behind.
Let's say that you had 3 little dogs and they get out every once in a while but they're really too small to do any real damage. One day they get out and only one comes back, so you go looking and see them in a cage in someone's window. You go knock on the door and ask for them back and the neighbor says "no, they came on to my property and pooped so they're mine now. there was also a third one but I couldn't catch him, I'll get him next time though". PEOPLE WOULD GO CRAZY! POLICE WOULD BE CALLED AND SOME PEOPLE MIGHT EVEN SUE! Why is it any different with pet chickens? Some might say it's because dogs are pets and chickens aren't, my answer to that: how dare you tell me that I can't love my chicken as much as you love your dog.
Some might say it's because dogs cost more than chickens, my answer to that: what if I found my dog in an alleyway stuck a box without a tag, and rescued him. Does that make my dog less valuable and pet-worthy than your dog?
Rant over.
I would go and ask for your birds back one more time but record it (discretely, voice recording in your pocket if would work too) say that you'll clean up any mess they made (a picture of said mess/their yard will be useful later) if they still refuse to give them back, threaten to call the police. If they STILL refuse, say "ok, I'll go call them now. See you soon." Turn off the recording right there (more than an arms length away so they can't take it away from you) turn around, and walk away. DON'T TURN BACK AROUND NO MATTER WHAT THEY SAY! You now have HARD EVIDENCE that they STOLE your birds and can call the police, with that much evidence they HAVE to listen to you. Now the pictures come in handy just incase they fake some damage that your birds "caused".