them carburetors are gonna have to come off and be cleaned/rebuilt .
3 year old gas has probably played hell on the jets inside the carbs and no amount of gum out will clean it out .
syphon out all the old gas and rebuild the carbs . take them apart completly and make sure each jet is cleaned .soke the jets over night in chemdip . the inside of the carbs must be super clean. their cant be any varnish or debri left in the carbs .
download a manual and take your time . after its back together , set all your adjustments on the carbs to spec. idle air screws and idle adjusment ,ect.
Letting the filter sit in a mixture of 50/50 oil and gas will clean it well enough. It's just a plastic screen, so as long as it allows enough fuel to flow you'll be fine. When it dries go ahead and spray it with carb cleaner or starting fluid. That'll clean it up real quick.
Draining the tank is easy. Remove the rear racks (4 bolts), rear plastic (a few rivets on the floorboards), and there are only 2 bolts that hold the gas tank in on the right (passenger) side. The tank and the cover will slide out to the right. However you'll need to remove the fuel pump before as it won't slide under the frame with the tank. The fuel pump has 6 8mm bolts holding it in. Once your tank is removed just spray it with water and blow it out with an air hose or let it sit a few good hours somewhere it can air out naturally.
I would suggest cleaning the pump by letting it run a clean 50/50 mixture of gas and oil or gas and seafoam. (I use oil for some extra viscosity). Plug the pump back up to the factory wiring, drop it into your prefered 50/50 mix and turn the key on for a few seconds to let it pump, then turn it off. Repeat this until you feel the pump is clean enough for your tastes. (I ran about a quart of gas/oil mix through mine when I had water intrusion issues.)