there must be a blocked oil way to the vacuum pump as its supposed to draw a little bit of oil into the pump and then be drained out via 1 way valve on the pump
so I'd check that the drain as well as the feed to the pump is free flowing with some compressed air
and if thats OK ensure that the 1 way valve isn't sticking
if regarding the heavy breathing then
thing I'd check is the crankcase pressure relief valve (PCV) these are sprung loaded and are only meant to 'burp' excess pressure every now and then. The exiting gas is piped back to the inlet, however should the valve stick open then the engine tends to suck the air out of the crankcase all the time and this carries oil over with it.
If you remove the air intake pipe and look inside where the crankcase breather is plumbed in you may find evidence of oil.
If you do find oil replace the valve