If it (turbo) was pouring oil in to exhaust it would be smokey. You've mentioned exhaust fitment it is quite possible residual oil from the new exhaust or installation perhaps. Oil in the intercooler is probably from the CCV (Closed Crankcase Ventilation) breather it is a typical find on all turbo diesels which don't have the oil separator (so called catch can) fitted. Typical bloody car manufacturers "cheap skating"!
Fit one ASAP.
The small hole on the base of the airbox is a drain/vent hole and it is on every unit. Feel free to work out an alternative for it but blocking it outright is also not the smartest thing.
Cheers