YOU CAN HANDLE THIS PROBLEM.
I have had great success with rat traps baited with small strips of raw bacon. Tie the bacon onto the trigger with twist ties such as are found on some loaves of bread. The spring required to make a spring trap effective makes the trigger relatively insensitive, so you can't use a soft bait like peanut butter. Use something difficult to remove, like raw bacon.
Actually, I suggest you try the Glue Rat Traps such as those available at Walmart. They are cheap and disposable.
https://www.walmart.com/ip/Catchmast...s-2ct/15723807
I recently had great success with a Glue Snake Trap which I bought from Amazon. The paperwork that came with it mentioned that it was effective for rats as well.
I wouldn't use poison. Rats sometimes die in the walls of the house if poisoned, and the smell takes a long time to go away.
I most certainly would not remove my citrus trees. I love both oranges and grapefruit. My late wife used to go out on a cold morning and pick some oranges off the tree, squeeze them, and we would have fresh, cold orange juice with breakfast.
Home Depot has new, unused five gallon plastic pails with lids for a few dollars. They work fine for storing birdseed.
One last word. Squirrels have the same affinity for birdseed as rats do. Your problem may be squirrels. Don't be surprised if you end up with some squirrels in your traps.