The best solution is to 'plug' up the access holes with a tight wire mesh, or repair any holes that are the result of chewing or whatever. At the same time, buy a have-a-heart trap from a Home Center like Home Depot. Make sure you get the smaller trap for squirrels. The larger one probably won't get set-off by the squirrel.
Also, rid the tree limbs allowing access to the house. (They're an insurance liability anyway.) I'd start with pruning before I'd cut down the tree(s) entirely. If you need any more info, post up.