Generally, when the gasket that Dick M. cited is missing, you can see oil dripping from the flywheel inspection plate and through the hole in the bottom of the flywheel housing as the engine is running. You say the oil doesn't leak when the engine is running, but does leak when the engine is shut off and a puddle forms beneath the engine. This is the classic loose rear main bearing leak syndrome. There is either too much clearance between the crankshaft journal and the Babbit bearing material, and/or the Babbitt material is broken. If the bearing thrust is shot, the crankshaft will move fore and aft as the engine is running. This causes oil to pump past the rear main bearing "seal" (It isn't a seal). Since you write that the oil doesn't leak when the engine is running, the thrust is probably o.k. But observe the crankshaft pulley anyway as the engine is running. Back and forth = worn thrust.
My bet is that at the least, the rear main bearing cap needs to be adjusted. If you don't also adjust the center main bearing, you are wasting your time with the rear bearing. The crankshaft "whips" as it spins, causing a flexing inside the center main bearing. When the bearing clearance becomes too great due to this whipping action, the rear main bearing will begin to leak.
Plan on spending a day or two adjusting all the main bearings, although the front main bearing rarely needs more than one thin shim removed, if even that. It is critical for oil leakage control that both the center and rear main bearings be adjusted in tandem. A pain in the you-know-what, but if you want to eliminate (for a while) those embarrassing puddles of oil beneath your car, you gotta' attack the main cause of oil leakage in the areas you mentioned. 'Might as well adjust the rod bearings while the pan is down. No better time than then to eliminate that annoying rod rattle. Take heart: Adjusting the rod bearings is a piece of cake compared to adjusting the main bearings.
Marshall