The quickest, easiest, and most effective way to get rid of a huge rat population is poison.
Last year we had rats so bad that I would see the BIG ones (12" long bodies) out during the day. They say the rats only come out during the day when there is a large population. Usually it's the smaller ones you see during the day because, being smaller, they can't compete for food at night. So you know if you see the adult (humongous, nasty!) rats during the day, you've got them bad!
I tried setting traps, I tried using the 'natural' solutions (peanut butter and plaster of paris, soda, cement or P of P mix around their holes) and NOTHING worked. Heck, I even tried poison and that didn't work at first. I lost adult bantams to the rats, numerous chicks and quail, adult and young pigeons, and even a few LF hens who decided to go broody in the wrong place
When we first started putting poison out we would use the bait bars and tie them down. That worked for the bigger ones but not for the young ones still in the nest. The young ones would come out after their parents stopped coming back to them, and the process would start all over again. Finally, the guy at the feed store told me that the delivery person that brought them the poison bait bars said that the poison is
most effective if you DON'T tie it down. If they can, the rats will carry it off and back to their nest. This way you get the adults and the younger ones who haven't started coming out yet.
After months and months of fighting with the nasty things, it took all of about a week to be totally rid of them by putting out the poison. Don't waste your time/money on anything else, if you have outside pets you're worried about, tie or pen them up until you get rid of the rats and put out as much poison as you can. The stuff I bought comes in a small pail...I bought 4 of them. It took almost 3 full pails to finally get rid of them but they ARE gone!