Like ChicKat said, have you ever thought of a compost pile? You don't need a whole lot of space, depending on the amount of waste you create, just plop a couple wood pallets up and you can pile it in there. Just turn it a couple times every now and then with a shovel, actually forget the shovel… your chickens can have a hell of a fun time digging in it for you.
Depending again on your waste and area eventually you'll get some nice rich soil you can then sell or use on your own garden. For me my open-style compost pile breaks down really fast, within a month, and I have the chickens go in and loosen it up every now and then so I can easily go through it to transfer some to the garden bed. As for the feed bags you could just burn them, but if you can recycle them I think it would be better to do that. When feed bags burn they send a lot of ashes into the air versus actually getting burned down, or at least with the ones I have, that's what I find… so I only tend to use them as a fire starter. I usually keep an empty bag to store hay strings in, maybe you also have a similar use for one? One down at least…
As for your rats, make sure you are keeping all of your garbage in an area that isn't accessible to them when you aren't burning them. You aren't leaving them piled up on the bonfire while you're waiting to burn them right? I think it's important to keep them stored separately where animals can't get into it. If you don't have a garbage can I recommend getting one so the rats can't tear the bags open if they're just sitting outside somewhere. They have to be eating something in the meantime while you've not been burning anything to attract them to the firepit… after all.
When you burn is the garbage getting burnt fully?
If not that's also a problem. Are the bags getting wet so they can't burn? My neighbours used to leave their garbage on our fire pit but naturally when things get wet from rain they won't want to burn. Even if the outside looks dry, if it's rained at all, all that moisture is going to accumulate on the inside so in the end the middle won't get burned at all. Even if it's been really hot, all that heat can create moisture to build up on the inside… if your garbage is piled fairly big.
If this isn't a problem, and the garbage isn't burning fully, then try to put garbage on slowly as fire can be snuffed out if there is too much on it at one time. So put only a couple bags on at a time and only put on more when the flames are big enough to cover them. This will make sure that everything burns out evenly into a nice pile of ashes for you. I also recommend not manually putting the fire out as it should burn out itself. I've seen some people regularly do this but if there's a flame that means there's still something to burn... Sorry if you already know this but I see it a lot so I wanted to make sure!
It's good you got rid of most of them by switching feeders! It would be a good idea to maybe run a skirt of wire down the side of the coop and block any holes up to prevent them from getting inside the coop first as well. Even if they don't find food from your chickens you don't want them continuing to set up camp if they can find another food source nearby. Do you have neighbours with potential food out? If the rats are smart they can also end up going for your eggs, and your chickens/ducks water may also attract them when it's hot out. Plus if you have other predators the skirt of wire is especially a good idea.
I also 2nd mint, however be careful if you use a spray as the powerful smell could also bother your chickens along with Weehoppers advice about the cotton balls. Use any sprays on the outside, not the inside, so the chickens can move away from it.
(Sorry this is kind of long.
) Good luck on getting rid of the rest of the rats completely!
