Could be a couple of simple things, but the pump reacts to the pressure change of piston going up and down to move the diaphram inside the pump which pulls fuel from the tank, and if oil is in the line, your oil level could be too high in the crankcase or you have one of the following problems.
Valves need adjustment pressurizing the crankcase pushing oil into that pump diaphram.
or
Bad head gasket pressurizing the crankcase thus pushing oil into the fuel pump
I suspect its a bad head gasket and its not a hard job to do and maybe $10 in parts for a head gasket and valve cover gasket. Taking off the valve covers is not hard, 10 min, and the head maybe 20-30 minutes so over all a couple of hours all done.
The valve clearance if I recall should be .004-.006 range. Take out the plug and stick a screwdriver in the plug hole and turn over by hand until piston is at the top. Then adjust the valves.