As for advice. We've tried live traps, poison (unfortunately the neighbors beagle found it before the rodents), but since this is a banner year for them all I can say is...do your best to lock them out, clean up after them with bleach as soon as you find it, keep food stuffs (dog/cat food and trash) out of their purview and try to keep nesting materials to a minimum.
Lock them out means get vehicles supplied with a 'screen', fill and block all holes on, in or near your house, and check behind appliances frequently for new scratches.
Pay attention to your cat! They will hunker down beside scatching places you can't hear and may even try to 'tell' you there is a problem. They may also use the area for a 'scratch' spot as that is one way they mark territory. Of course, some cats are so domesticated as to befriend and ignore unwanted guests. But most will not appreciate their boundary being violated.