On another forum I frequent, a guy has been shooting at red squirrels that have overrun his yard and house to no avail and asked for other suggestions to get rid of them. A few replies:
Bucket o' water with birdseed floating on top. Fill half way, float the seed, check daily to remove carcasses.
Works on chipmunks too.
I shoot them with a pellet rifle at every opportunity. Hate the damn things. If you keep a trap set all the time, you can shoot the one in the trap the first thing you do in the morning, and then blast any you see all day. You will never win the battle, but you can keep the herd under control.
A slight addition to the bucket bird seed trap is to use a dowel (or hunting arrow) stuck through the lip of the bucket with a soda can skewered on it. Yes you have to drill the bucket to do this. Smear peanut butter on the soda can and make sure its free to spin. The critters go for the peanut butter and fall in the bucket of water. This is very effective for mice and squirrels. If you have to do that in a hunting camp that is unoccupied for a few months each year, use antifreeze rather than water, it pickles them so they don't smell so bad. But don't use anti freeze near the dogs obviously.
I had a squirrel problem, they would do the same thing, get in my attic and nest in the insulation. I live in town so shooting is out of the question. My dog would love to get them but they just run along the top rail or my cedar fence and get away, teasing her as they run. I cut a piece of Lexan about 1 foot square and put it on the top rail between two of the pickets. When I see a squirrel in the backyard, I yell at the dog "GET THE SQUIRREL!". She tears out the backyard, they jump up the fence and haul ass along the top rail...until they run into the lexan at top speed. If that doesn't break their neck, the dog gets them when they bounce off the ground stunned. I haven't caught it on camera yet but it's hilarious. I have to move the lexan once in a while because they figure it out but that's minor. Smug little bastards. I feel like Bill Murray in Caddyshack.