I do a lot of hiking deep in the woods of northeastern PA, usually to where the trails peter out and then there is just forest. Sometimes, I will find some weird kind of folks at the parking areas, or a little ways into the woods, sometimes I find some weird folks deep in. My dog has been attacked by another hiker's dog once. After that incident, I started carrying bear spray (a large canister of pepper spray) that rides in a "holster" type device that is held in place by light straps that go around my shoulders. The canister is positioned at the middle of my chest so that it can be fired from that spot, or quickly removed from the harness and held in my hands. I also carry a pistol. I can say, having gone through the situaiton where my own dog was bitten by another hiker's dog, that even if I'd had the pistol back then, I would not have shot another person's dog. Maybe if it was lunging at me, but to shoot someone's dog only escalates the whole situation. I've also heard that shooting dogs is not so effective at stopping them unless you hit the brain, and of course, you need to be certain you will not hit your own dog at the same time through a missed shot or overpenetration, etc. So, the bear spray is a good optrion, but again, you need to avoid squirting your own dog.
ANYWAY, if I came up on this same "crazed mountain man/homeless man" with his dogs and his screwdriver, etc, I'd deploy the pepper spay as a first line defense and only draw the pistol if the situation was not contained by the pepper spray. Everyone knows that pepper spray is not totally effective and may just make a drug-crazed person angrier, but then, hey, there you go, he's angry, not stopped by sub-lethal force, intent, opportunity, ability, etc. Shooting warning shots is a waste of ammo. Shooting someone's dogs is a very good way to make an angry, irrational person even angrier and thinking even less clearly.