I agree with Marty, Sounds like the Draft vent, If it is then it is probably connected to the valve cover, It allows combustion gasses that get by the rings and enter the base of the engine to escape, On older pre 1961-62 cars they were called road draft tubes, They faced downward and the idea was that combustion gasses were siphoned out of the crankase as the vehicle travelled down the road, If gasses are not vented then the engine base would eventually become pressurized from normal ring blowby and possibly blow you pan gasket, Road draft tubes were replaced with PCV Valves(Positive Crankcase Ventilation) which basically is a vacuum line from the intake that sucks off the base gasses and directs them thru the manifold to burn them during the combustion process reducing emissions and creating a closed loop for Positive CrankCase Ventilation.
The tube as it is called is a draft tube to reduce base compression so it would be normal to see some amount of escaping gasses coming from it including an occasional small drop of oil, More when the engine is being run at higher rpms or working hard,Excessive smoke/steam/gasses accompanied by dripping oil indicates excessive base compression caused by worn rings or broken rings,blown or leaking head gaskets.
Excessive dripping of oil without excessive blow by can be the result of clogged oil galleries causing the valve cover to fill with oil and escape thru the draft tube
If the smoke occurs for more than a few seconds after the engine has been shut down it could also mean that the engine is running hotter than normal causing the oil on the inside of the engine to smoke or steam from contact with the hot metal engine parts
