I agree with every post here.
Just want to add that I would definitely be getting in touch with the local Dept. Of Conservation. If you don't have remains to show them at this point I hope you have pictures. They really need to get involved with this and the sooner the better. Any pack, either wild dog, hybrid wolf/coyote, hybrid coydogs, wild dogs that would do this much carnage in one night would not hesitate to take on an unarmed human or small child.
I think you have a bigger problem here than one with the livestock. I think you need to get to the base of what it is and in the mean time, put up hot wires, traps and lock and load whatever weapons you have.
Also set out game cameras and get proof of what is hanging around and get rid of it. The sooner the better.
My heart breaks for you and your neighbors. Good luck.