Well, You can use the glue that comes in tubes to trap mice. All you've got to do is smear some glue on a piece of thick hardboard or a small piece of carpet and leave it in their path. They'll just stick to it when they walk over it. They usually end up freeing themselves so you have to quickly put the mats in a box and dispose it off the way you like.
They make traps that are disposable. You can set them out, and they can't get out. There are also pellets that you can use, they will eat them. Other than that, there isn't much else you can do unless you get an exterminator in there. I myself would keep the cat, during the day, let it out to go and get rid of the mice for you, just bring the cat in at night, so you aren't going to get the 'surprises'. Hope this helps, good luck.