The idle adjustment screw adjusts the throttle linkage and ultimately yes, the throttle plates. Idle adjustment determines the proper RPM's when your throttle grip is at rest.
The throttle stop screw should be adjusted to keep the throttle plates from closing all the way, so the engine won't die even if you adjust the idle screw all the way down.
The fuel/air adjustment screws are what determines how much air is mixed with the fuel, or how lean or rich it runs. There is a fuel/air adjustment screw on each carb, and they should be synchronized.
If you can't get your idle adjusted properly then it's usually a problem with the fuel/air mixture. This can be affected by improper screw adjustment, vaccum leaks, clogged idle circuits, lots of stuff.
If it was me, after sitting a lot like you describe, I'd start by removing the float bowl drain plugs (if so equipped) and all 4 fuel/air mixture screws. Then take a can of carb cleaner with the litte red straw and squirt it up through all 4 empty mixture screw holes until it runs out the drain holes. Leave it set and do it again. Then clean and replace all the screws, turn them all the way in, then back each one out 3 1/2 turns. Replace the drain plugs (if applicable) and prime the carbs with fresh gas. Fire it up and see if it idles smoothly, and if the RPM's go up and down properly when you turn the screw. If it still doesn't, then you'll probably need to pull the carbs for a thorough cleaning with the float bowls off, adjust the float heights, make sure all the jets and circuits are cleaned with carb cleaner and blown out with compressed air.
Also make sure all your vaccum lines and hoses are plugged in properly and there are no vaccum leaks around the intake boots or manifolds. Vaccum leaks usually cause a high idle though. Your problem sounds more like it might be too rich. Pull your spark plugs after idling a while and if they are black or very dark or even wet, then you aren't getting enough air mixed in with your fuel.