Keeping mice out of our house...

We recently moved back into our house (which we had been renting out) and found A LOT of mouse poop in the kitchen. I bought traps and in 10 days have caught 3 mice. In the mornings, I can smell urine or spray when I go into the kitchen (some mornings worse than others), but don’t find poop anywhere. The current trap had been baited and ignored for three days before catching this latest mouse. To me, this means it was a mouse entering the house for a visit, versus mice living in the house. Is this wishful thinking? I keep remembering all of the poop I found on the stove and thinking that it must have been caused by a lot of mice.

Additionaly, I keep reading suggestions to fill up the holes on the outside of the house to keep mice from getting in, but I guess I don’t understand what kind of holes to look for. Also, it would be fairly easy for mice to get in under our house because the crawl spaces are not sealed in anyway. Is this something to worry about?