Biggest thing you have to watch out for with wild rodents is the possibility of chemical contamination of the bodies. Some of the poisons may have been ingested by the mice, but not in sufficient quantity to kill the mouse. The problem is that some of these poisons can be cumulative in reptile vital organs, and after a while build up to a toxic level.
Best rules for eliminating mice:
Find out what they are coming in for, and make it impossible for the mice to get to. If it's food, make sure all foodstuffs are stored in mouse-proof containers. If water, seal all leaks and make it risky for the mice to get to your normal pet's water dishes.
Use a variety of traps. Mice aren't stupid; I've seen them run right towards a sticky trap and leap over it. If you're using a snap-trap, try baiting it with a mixture of rolled oats and honey. I've also heard that peanut butter works well for them.
If you use poisons, make sure your pets cannot get to poison or to the carcasses of the mice. Poisons aren't selective, and they don't vanish from the bodies after death.
Seal holes and access points into the house. Check those sealing jobs frequently, because the mice may chew right back through. They're persistent little beasts.
Show no mercy. Mice can be mighty cute, but they are also mighty destructive. They will chew up stuff to make nests, and they will urinate on just about everything they walk on.
Good luck. It took us a while to get rid of the little vermin.