Ive pulled lots of freewheels apart and the advice here is good. If your re-building a FW, use grease to hold the bearings in place (I think theres around 45 a side...) but once its built use oil.
The amount of 'broken' FW i've pulled apart only to find thick heavy grease inside is amazing. The grease holds the pawls flat against the body of the FW and doesn't allow them to 'spring out' against the ratchet (toothed) ring.
People think no clicking noise and no catching - FW broken. It takes A FOOKIN LOT to break a FW.
The pawl spring that flicks the pawl against the outer ring is very weak and is a large cir-clip type ring the thickness of a small paperclip.
To clean a FW soak it and shake it about in petrol, dry it then squirt some oil in there. Bed it in by putting it on the end of a drill chuck, hold the teeth and spin it......add to bike. Ride.