I had a major oil leak problem when I bought my shadow (1994, 2.2) It was leaking from the valve cover, PVC valve hose and crankcase hose.
Both hoses were cracked and i'm sure the gasket for the valve cover was bad. So I replaced the hoses and PVC valve and replaced the valve cover gasket (after cleaning the surfaces, Then changed the oil. It seems to be happy now. I suggest you also check the oil drain plug and oil filter for corrosion or dents. Your oil pan might be corroded as well.