Mice are very flexible and can squeeze through the smallest of holes, even gaps under doorways. They also don't necessarily choose dirty or unkempt homes. They can get into the walls, and get into pantries and cupboards (as you found out) wherever there is food available.
Mouse traps do work. They even have a lot now where a mouse will go in and be trapped alive. You can then remove the mouse without killing it and "relocate" it. Don't get the glue trap kind, though, If a mouse gets his foot caught, he will likely chew it off to get away. And, that's just cruel.
Also, check around your house for ways they're getting in and block them up. I bought a house a few years back and found evidence of rats in the attic. I could also hear a scratching sound in the walls at night. Every now and then, I would see rats scurrying along the phone lines to my house. That's when I realized they were crawling along the wire to a corroded attic vent that had just big enough of a hole for them to squeeze in. So, I put up a new vent cover and that solved the problem.
BTW - things like steel wool and foil don't deter rats or mice. They just chew right through it. They even have been known to chew through electrical wiring. You have to use proper metal grates and screen mesh to keep them out.
