Any good degreaser will work.
About the cheapest is to buy a gallon of cheap Wal-Mart paint thinner.
TAKE IT OUTSIDE away from flames or pilot lights.
Put the disassembled parts in a pan or coffee can and cover as much with thinner as possible.
Let soak for a while, then use bottle brushes, toothbrushes or whatever you can find to scrub all the gunk out.
When clean, flush with clean thinner, then dry by blowing with compressed air, or by shaking them and drying with a hair dryer.
After the parts are clean, apply a good rust preventing lube like CLP Breakfree to a clean toothbrush and "scrub" the parts to apply a thin coat of lube.
Use CLP on a folded piece or paper towel soaked with CLP to lube the springs.
