Remove the bird feeders. There is nothing you can do to keep the skunks away other than removing this food source. Put up a bird bath instead to enjoy busy and happy bird activity in your yard. Keep a hose handy for daily rinses and fill ups.

I am fully convinced that my birds enjoy the bath more than the feeder!

You might try rat traps baited with peanut butter. Put the trap up where the dogs and cats can't get to it, and throw away the trap when full. A rat trap costs only about $2, and can clean up a lot of problems. You might only need to trap once: the other skunks might be detered by seeing one of their number killed.

Since skunks are about the size of a large cat, I think a rat trap, even a big one, would only make them angry. I DO know what angry skunks do, do you?

The rat traps do catch the skunk (work ok on squirrels also). Rat trap springs are strong enough to do serious damage to a skunk, and hold it while you finish it off. The key is to get the animal held so you can finish it off. The birds don't mind eating the remains. Yes, the skunk may spray, but you can dispatch it from a distance (I like a shovel to the head.), and avoid the stink.