Rats in the bird shop HELP!!!!?

I volunteer for a non profit parrot rescue that has a serious mouse infestation. There are 2 sides to the building and on one side, we are tearing down the drywall (which has numerous holes in it) to limit the places they can hide. We have about half of of the wall done so far and now the mice are invading the other side of the shop! They terrorize the birds and we need to get rid of them most ricky tick! I have looked at many different traps and deterrents but I'm not sure which would work best to get them to get out and stay out. What is the best way to get rid of a REALLY bad infestation? (I estimate their numbers to be several hundred)