Tell the police that these dogs have already killed your stock and have threatened you. Ask what the law is in your jurisdiction for dealing with loose dogs threatening people or property. In some jurisdictions, you are entitled to shoot predatory dogs, if necessary, but in other jurisdictions, you cannot. If the police or animal control give you an answer, ask if they can give you the statute number, and then keep a record of what that answer was, and which officer provided it, and when, just in case it comes down to a drastic solution. Stay within the law, and document the steps you took to avoid drastic measures, down to dates, enforcement personnel involved, and descriptions of the incidents.
Take pictures of the dogs in your yard, especially if you can get numerous pics of them about the chicken run.
If the dogs are not aggressive towards you, you might just want to pop them in the car and give them a lift down to animal control every time you find them in your yard
... or just secure them out of sight of the owners, if possible, and have animal control come to get them. Your knucklehead neighbor might decide it's cheaper to fence in his dogs than to go to the pound and pay "bail" every week, and if his dogs run the neighborhood, and you're selective as to when you have them hauled in, he may not even know who's doing it. You'll also start establishing a record of just how often his dogs have been "in the system" for being at large.
Worst case, and if all else fails ... if you live near your county line, take them to the pound in the adjacent jurisdiction, sans collar, and tell them you found it loose on whatever highway is just inside their county line. Odds are, the neighbor may not think to check adjacent jurisdictions for his missing mutts. At least the dog will have a chance of a better owner ... beats getting a dirt nap from an angry neighbor, from the dog's perspective.
Good luck, and be careful.
