I've never heard of setting rattraps for woodpeckers, or shooting them. I do have an acquaintance who had his garage door torn up by a buck's rubbing. Also in grooves of the siding.
They hammer on my roof sometimes. It doesn't hurt anything and makes lots of noise considering the fact that I've got a metal roof.
"If a shotgun isn't an option, rat traps can be baited with suet and nailed to the siding with the set spring in the top position."
Two words: Peanut. Butter. Works on Woodpeckers eating your house, works on rats in the chicken coop and draws just about anything you want to trap and move with a Hav-A-Heart trap. :)
I'd have a hard time killing a Woodpecker, though. I have my "little buddy" that's at the feeder every day for his "suet fix." Luckily, I have aluminum siding on my house. ;)
I've seen plenty of these three species in trees but never heard them on the siding or roof.
I saw a downy woodpecker just a couple days ago about eight feet up in the tree.