Mice can get in so many different places it is tough to seal everything up. If you are pretty certain you DO know where they're getting in, or at least where it is that you have seen them, set those dang traps. Gang them up in rows of 2-3. (Mice jump over the first one. SNAP!) Lay them lengthwise along edges of walls as mice don't like open spaces. They will continue to follow the scent of another mouse, so once you figure out the trail, you can whack their little heads off pretty quickly. (Yeah, I know you're the Farmer's Daughter and not the Farmer's Wife, but it works for everyone in the family!)
Peanut butter is good, bacon fat is good, anything that consistency that is protein seems to work well on the traps. I HATE dumping them out, so just buy a bunch of traps and throw them out with the mouse. Gomez used to keep a plastic bag in the basement (not here!) and would dump their little carcasses in there. I found the bag one day, picked it up and knew immediately what I was holding. NOT a pleasant sight...
I don't like poisons because you don't know where the mouse will keel over. Traps in the basement/attic/under the kitchen sink are pretty effective. This inward migration is usually only a couple of weeks. If you can block off the holes to the outside, so much the better. Steel wool around pipes into bathrooms & kitchens is pretty good, the mice eat thru almost everything else including that expandable foam.
Cats aren't always effective, some just don't care.