I got a couple of heart traps from animal control for a refundable deposit. Baited them with corn - set them on my property. I caught 12 chickens in 5 days. I brought them out to the country where there were woods and fields and set them loose.
I am all for getting rid of pests, however, I have never agreed with re-locating the critters, no matter what they are. You are just giving someone else the problem. NO THANK YOU!
The Hav-a-Hart traps are good to catch critters with, however once you have the critter in the trap, you should drop the trap in the pond for a while, then later remove the critter and either bury it or send it with garbage collections.
You have some options. You can chase the critters off every time you see them. Takes full time vigilance to do this. You can trap them either with foot traps or Hav-a-Hart traps, or shoot them. A nice break barrel pellet gun works wonders on things up to cat and chicken size. Legal in most areas.
For sure chickens are edible. As noted, if it is an older bird, just cook it slowly until tender. It will make excellent soup.
I am sorry, I don't have much patience for stray critters in my garden. I once took out 5 peacocks in one spree with a 12 gauge shotgun. I am sure the neighbors all heard the noise, but nothing was ever said. You think a few chickens can mess up a garden, you should see what 5 peacocks can do.
Owners of cattle or horses will take responsibility to keep them in, but for some reason owners of birds don't seem to take it very seriously. I would never shoot someone's cow, but once they have been notified about birds, I will deal with them if they continue to be a problem.
I grew up on a ranch in Northern Utah and we had all sorts of wild critters bothering livestock at times and raiding our gardens.. Not to mention stray dogs harassing livestock. If we were to protect our livestock, it took firm measures. A loaded gun was always close to hand.
I am sorry if this seems harsh, but sometimes that is what it takes to protect our stock and crops.
For you in city lot situations, it may be better to use the Hav-a-Hart traps.
These are effective.
work well too, but are bad for pets if they get in them. I use foot traps by my beehives for skunks. No bait. Pets stay away from the bees, but the stupid skunks like to eat the bees. I tie the trap to a ten foot pole and once I have a skunk, I lead it over to the canal and drown it. No stink doing this. They won't spray as you lead them away and the water carries off what ever they release as they die.
Gardening at 5000 feet elevation, zone 4/5 Northern Utah, Frost free from May 25 to September 8 +/-