RATS!!! on birdfeeders
Rats are not something we hear a lot about as birdfeeding pests. Squirrels and starlings, yes. (I am overrun with chipmunks this year, getting in my feeders.)
Have you tried putting up squirrel baffles to keep them from climbing the poles? That worked a charm for keeping the chipmunks out of my feeders. I'd also recommend getting cage-type feeders that are all metal. I have one that is a ball shape that's good for keeping out squirrels. They can't even reach in through the wire openings to drag out seeds.
Another thing you might try is taking the feeders in for a while and seeing if the rats lose interest and move on elsewhere in search of food.