Why does a tailpipe emit oil?

That doesn't sound good. These symptoms are a good indication that your piston rings are gone or you have a damaged head gasket. With worn piston rings oil is allowed past the piston and into the combustion chamber allowing it to be burnt with the fuel air mixture, this also allows combustion pressure to be leaked into the crankcase pressurising the engine and forcing oil out from any older perished gaskets. However the same symptoms can be found by having a damaged head gasket where the oil gallerys between the head and the block that are normally sealed together by the headgasket, leak and allow oil to enter the cylinders and be burnt. In both instances it requires a lot of expensive mechanical work to recondition the engine. There are additives on the market that thicken the oil and lessen the amount of smoke but are only a band aid solution and won't save you from an expensive repair later down the road.

Notwithstanding the above answers, a common cause on modern engines is the failure of the turbo seals. Oil gets sucked into the inlet manifold. There is often too much to burn so it gets blown out the back. Take the hose off the intercooler; if it drips oil suspect the turbo.

Whatever the cause, the catalytic converter (if fitted) might also need to be replaced.