Don't Feed the Animals!

We are having a problem.  A predator kind of problem.  I'm not sure what kind of predator, but I have lost several (15) meat chickens, and both of the turkeys.  I lost a few laying hens as well, but those were eaten by the next door neighbors dog, when they wandered through the fence into his territory.  The yard is fenced in, with smaller gauge wire, and is 4 plus feet high in the back, and 5 feet in the front.  Can coyoties climb fences?  We are thinking maybe a racoon?  The thing is, some of them were taken over the fence and eaten, and some of them were left dead in the yard.  *Sigh*.  Trying to figure out how to solve this problem.