Now that we know we have rodents we're going to have to figure out how they're getting in, and put out either live or snap traps until we can seal the places they've been intruding through.

Poison's out because if we've got burgeoning hunters we don't want them eating a poisoned one, and glue traps are just evil. Snap traps, as much as I don't like to kill other creatures, are at least humane in that the rodent usually dies faster than it would being tortured by a cat.