I use 90% Isopropyl Alcohol (rubbing alcohol) on a small Hoppe's square with the provided cleaning rod for AEGs. After a few swipes, using a fresh square each time, I run two dry squares through. After that, I moisten another clean square with some 50 weight silicon R/C shock oil and run it through. Another dry square through to remove excess, leaving a very tiny ammount of silicon, and I'm done.
When I do this, I clean the hop bucking with spray silicon (very low viscosity compared to the shock oil) and a Hoppe's square. Then, I wipe it several times to remove any silicon that may remain. Some guys spray the stuff in there, which only reduces the sticky effect of the rubber bucking. This reduces the hop-up effect, and makes it inconsistent.
I clean the hopup chamber itself in the same manner as the barrel. Q-tips can be used here rather than the cleaning rod/cleaning squares.
For gearbox lubrication, alot of guys use white lithium grease which is available at any hardware store. You might have to get it in a larger cardboard tube, but it's all the same stuff. What I use now, however, is USGI M14 grease. It comes in small plastic cups with a yellow cap, and is available at gun shows for less than a dollar. Raith gave me some, and said he heard about it from Harley. It apparently stays-put better than white lithium, and provides more durable lubrication for your gears. Use it sparingly.