I have a Cessna 172XP with the 195 HP Continental IO-360. The engine
runs great but is at 1400SMOH and is approaching TBO.

From the bottom of each cylinder head there is a small aluminum tube.
These tubes are manifolded together on each side of the engine and
routed down the firewall to vent overboard behind the cowl vent.

I am getting some oil dripping out of the tube on the pilot's side
after shut down. Also, I think both sides vent some oil in flight
because the belly gets especially oily after a few hours. Overall I
use a quart of oil every 7-10 hours. (I have an oil separator on the
breather tube and I don't think I have oil exiting there.)

What is the function of these tubes and what condition causes oil to
leak from them?

Thanks,

Jeff