I'd suggest reading Sheldon Brown on freewheels and free wheel lube in particular. The article says use oil, not grease for the pawls. Being a piigish sort, I generally get the wheel parallel to the ground and using an oil receptacle with a tiny spout, dribble the oil in to the space between the gear and the core while spinning the wheel slowly. Then let that seep in and repeat.
Freewheels are generally fairly cheap and have 2 or 3 pawls. White industries makes a high quality freewheel that is made to be rebuiilt and last for a long time. They are not inexpensive.