One of our homes we lived far out in the country, very wooded, area. There were a lot of gray squirrels. If they can get into your home, they will during the winter to raise their young. They will chew through drywall, chew wires, chew anything plastic (tools, fence insulators, etc.), and make tons of noise all hours of the night. We also had issues with chipmunks doing similar things under the house. The best course of action for the chipmunks is cats, and sealing up every ingress into your home. The squirrels you need to seal all around the house so there are no holes to invite them in. Loose soffit, loose flashing, etc. they will tear through. This isn't a joke, they will do a lot of damage. Cats will not bother squirrels most of the time because they are too fast and agile for the cats. Dogs are better to scare them off.
As far as getting rid of squirrels, seal up the house, do NOT feed them anywhere near the house (if you feed birds, have squirrel proof feeders 50+ feet AWAY from the house), get a dog, remove trees that are close to your house if you can. There may be other methods to deter them, but many may be illegal outside of hunting season. During hunting season, I would suggest an air powered break action .177 pointed pellet riffle as it is much safer and you are already close.
I have seen a lot of damage by them over the years. Our neighbors at one home had maple syrup lines and the squirrels chewed through them in the woods and cost them thousands of dollars of repairs. Granted, that was the squirrel's turf, but your home, they're cute little buggers, but can do a lot of damage (including burning your house down if they get through a wire, and they will stupidly try). Good luck.