I live out in the sticks too. 6-8 large dogs could do some serious damage to your pets, livestock, and humans! First thing I would do, is to call the Sheriff's office, and tell them you want to file a report, a written report, so it will be on record. Most times here, if you call them, they tell you to deal with it when referring to livestock. These dogs are a real threat to your personal safety, make the Sheriff aware of this! Years ago, I had trouble with the two-legged variety of trespassers, one of whom was stalking me and my children. The Sheriff's deputy came out, and asked me if I owned a gun? Yes. He told me I had every right to shoot, as long as they came into my house. Since then the laws have changed, and if you fear for your life or your family's, you have the right to shoot. I don't ever wish to take a human life, nor one of an undeserving animal; but if push comes down to shove, it isn't going to be me down in the dirt! If the Sheriff won't come out and talk to the neighbor, then I would get a Game Cam so pics can be taken 24/7, even when your aren't home. If I caught the dogs on my property, it would be a SSS situation...period. Don't tell anyone! Don't threaten the neighbor, as obviously he is a nut job. Remember, you have to live there with the neighbors, so the less confrontation the better. Save any and all dead animals that the dogs have destroyed and the camera pics, because otherwise, when the neighbor finds his dogs missing, he may call the law on you!! If he comes knocking on your door and asks if you've seen his dogs, just tell him no.
Luckily, I have decent neighbors, none too close, and we all follow the rules of the "country". Any loose dogsfound harassing or killing livestock will be shot on sight! That's just the way it is, and we all know it and respect it. Good luck, stay safe!