they would either be tunneling in through the floor, or getting in a gap, what size wire did you use, as already stated unless you can keep the floor free of spilt seed, then your going to get rats,
I'd suggest getting yourself a few mk4 fenn traps, look on the trapping section for places to buy, and best methods of setting them, build tunnels either from wood or brick/slate, to hide the traps inside, stops next doors moggy getting caught, and re build your avairy,
would suggest you steer clear of poisons, as unless you know what your doing, you could get into all sorts of trouble