Holes the size of ping pong balls may not be rats. They may only be mice. Not as bad, but really not something you want hanging around either.
Whatever the case, steps in control are to rat proof the structure and also remove access to food and water to the vermin. This all takes a lot of work. Spilt feed on the ground is likely what attracted them and will sustain them, so if that is going on, whatever feeder or feeding method you are using will have to change. Perhaps hand feeding only what the birds will eat. All else gets taken up and stored in METAL containers. I used a rat proof treadle feeder on my mouse problem and it went away.
If you do decide to go "kill em" route, be thinking poisons in proper bait stations.....the kind with pins in them to hold the bait blocks in place so nobody drags one outside where your birds, pets, kids or other unintended targets might find them. As near as I have been able to find out, the risks to birds, pets, etc. from poisoned rats is not as bad as some fear, but the risk of exposed baits that have not been washed through the rat first is.
Start with one of the anticoagulant baits, which may take 5 days to a week or so to see some response. It has to accumulate over time. You can monitor it by how fast the bait blocks go away. Then when that dies down, switch to a fast kill / one bite block to pick off any stragglers. If you do have rats, most likely they are brown rats (aka Norway rats), which often times are too big for traps to nab. You can try trapping, but don't expect much success from traps. Traps alone won't cut it. Most rat colonies can populate faster than dumb rats can be trapped.....or at least they can keep up with no sweat. Rumor has it if they sense a drop in numbers, they get busy in the bedroom so to speak so as to catch back up. They are that tough to deal with.