I use snap traps, covered with a wooden box with rather smallish holes when outside to prevent that bunnies or birds get in. They are smart though, I also use a DIY marten live trap when they figure out to avoid the snap traps. Nuts, bread, nutella, neapolitan wafers used as bait. Be sure the traps have quite some punch, I've got some that are just suitable for mice.
I pretty much have just single rats moving in now and then, but last fall one killed 4 kits out of a litter of 5.
A wildlife camera is a very useful tool to see if there are such critters, or which (turned out to be a dormouse once) and what they do.
