This is kind of vague so I'll answer the best that I can. These two symptoms (liquid out of the exhaust and liquid dripping from the turbo inlet) might be unrelated.
If it's oil at the entrance to the cold side of the turbo it's likely coming from the valve cover vent/PCV that connects to the intake snorkel(a certain amount of oil pooling in the intake/turbo is perfectly normal). Your PCV valve might be bad if its excessive. Most people resort to a catch can with a filter to stop oil vapor from pooling in the intake tract.
It could also be the turbo oil seal is shot. The turbo oil drain line could be clogged or the oil is overfilled (either would keep the oil from draining properly from the turbo, allowing it to leak).
Have you been using any solvents in or around the engine? Run through any big puddles or flooded streets?
Or you could be dumping gasoline and it's picking up soot(could be running extremely rich). It could also be a lot of gasoline in the oil(blowby, clogged PCV valve) and it has thinned the oil significantly.
The most important thing to do first is drain the oil and clean everything you can get to then refill with fresh oil. Replace the PCV, oil filter, etc. Replace or check your air filter to make sure it's not clogged up(causing a higher vacuum than normal). I would also consider pulling the downpipe loose at the front to see if its wet. You could also pull your plugs and check them.
What is the consistency?
What does it smell like?
Does the car smoke when running at normal operating temps?
Does the car smoke under boost?
If so what color is the smoke?
Depending on the climate most cars will have some condensed water vapor in the exhaust upon starting the engine. Too much water coming out of the exhaust could be a blown head gasket and it will pick up some soot. Are you running pure water in your radiator or a mixture of antifreeze/water? Antifreeze will create white smoke as it heats but water will not.
