Steel wool worked for me. I pull out my fridge and range every few months and used to find mouse droppings. Since I plugged the holes with steel wool, I haven't found any. I guess my cat wasn't very threatening.

I found a possum inside once too, helping itself to cat food-it had come in the cat door. Closed that up as well. lol

Mice can get through holes about the size of a pencil. I've had good luck over the years with stuffing the holes with a coarse steel wool and then using some spray foam insulation to keep things in place. Basically stuff the hole fairly tightly with steel wool and then stick the tube of the spray foam can into the steel wool and give it a little blast. The foam expands around the steel wool and sticks to everything. It's not the most attractive thing but it works. They also now sell spray foam with some kind of bitter or spicy additive that discourages animals from chewing it but I've never used it.

Carefully inspect the perimeter of the house, looking for any holes or penetrations for things like air conditioning refrigeration lines, electrical lines, etc. If you have an attached garage, then check the bottom seal of the door for a tight fit.