I am losing oil (crankcase, 5/30 w.) At the rate of 1 qt. Per week. It is not using oil but is spraying underneath the car but only on the right side(passenger side) but only while driving. When it is parked there is no leakage. I have checked the most common reasons (valve cover gaskets, oil pan, oil pan drain plug, cam and crankshaft seals) It is like a high pressure oil line has failed while driving (engine pressure--?) And when I stop and check underneath, it is dripping motor oil. I clean it off and the same thing happens next time it is driven. There has got to be a way to pinpoint this perplexing problem but I do not have the expertise to solve this mystery. It has a 3.8 L. Engine and an automatic transmission.
There's two ways to find the source of a leak. One is to add a small bottle of dye to the oil, then search with a black light. The dye will show up as a bright yellow stain that you follow back to the source. That doesn't work well though when the leak is as fast as it sounds like because the oil and dye will be everywhere right away.
A better alternative is to use a smoke machine to inject a white non-toxic smoke at 2 psi into the dipstick tube, then watch for where it sneaks out. A student found six leaks on my '88 Grand Caravan that way including a camshaft seal, valve cover gasket, and distributor adapter o-ring. With every repair the leak got worse and appeared to be a leaking rear main seal. After looking closer we found a pinhole rusted in a high point on the oil pan. Fixing each leak caused pressure to build in the crankcase and help push the oil out of that hole faster. You might find a smoke machine at an auto parts store that borrows or rents tools.