Mice are incredible opportunist creatures. Able to creep through very
small holes.  The most efficient way to deal with mice is with a
weasel. Natures own mouse killer. Sized only slightly larger (though
markedly longer) than mice, the weasel is a blood thirsty killer that
needs to eat a lot. Relatives of the weasel include the mink, the
fisher, the otter, the wolverine, ferrets, polecats and skunks. Ferrets
can often be gotten as pets (with the musk glands removed).

Places of entry are myriad. Remember it doesn't take much of a hole,
and mice, being rodents like to chew on things, and they will chew to
enlarge a hole. For example they can chew at the weather strip on the
doors, and come right in that way. Sliding door (especially near the
back) seems to have a slight opening even when closed (at least on my
Westy). Air ducts are another favorite.