Bottom line is they reproduce at amazing rates. Traps aren't going to catch them all, and the ones who live, again, reproduce. It's a cycle that has you beat I'm afraid.
So where does that leave you.. Well you can have an exterminator come in who can try and locate their nests and bait those, but if there are quite a few and inside walls, that will get messy and might cause damage to drywall... He can set poison traps they take back, but then you end up with dead mice in the walls... You can try those electronic controls like this
Electronic pest and mouse repeller(ultrasonic) for rodent pest control, mice, rats, mouse, and other insects, coupled with good house management (leave no food or water available) and you might see some results that way.
Or you could go and find a good family friendly breed of cat like a Ragdoll
Welcome to RagsGalore Ragdolls
Then let it take care of the mice and have some fun doing it.