Pilot reported loss of propeller control and engine oil pressure resulted in an air turn back and precautionary landing at departure airport.

Narrative

IFR departure from ZZZ; Mooney M20C; weather: wind 190@8 knots; VIS 10; skies clear; Pilot Flying in left front seat and passenger in front right seat. Provided a passenger safety briefing using the SAFETY acronym. Run up checks completed; no issues noted. Pre-takeoff safety briefing completed including runway to be used; type of takeoff; V speeds; actions and runways to be used in case of engine failure or mechanical concerns. Takeoff safety briefing and surface winds both indicated a favorable emergency return to Runway XX; as this would require less than 180 degrees of turn to line up. ATC cleared for takeoff Runway XYR; verified correct runway; applied takeoff power; verified engine RPM and manifold pressure correct; verified all engine gauges in the green; verified airspeed alive. Rotate at Vr 70 mph; then pitch for Vy 100 MPH; approximately 50 feet AGL detected uncommanded engine RPM increase exceeding 2;700 RPM. Pulled the propeller control to reduce RPM; detected this had no effect. Reduced manifold pressure in order to reduce engine RPM below red line. Informed ATC of a mechanical issue and need to return to the airport; now passing through approximately 300 feet AGL. Instructed by ZZZ Tower to make right traffic Runway XYR and read back the instructions. Moments later noticed engine oil pressure reduction to near zero pressure. Combination of low oil pressure and lack of propeller control suggests an engine oil leak in the governor system. Decided it was prudent for safety of flight not to fly standard traffic pattern as instructed by ATC out of concern of low oil pressure possibly resulting in engine failure during the several minutes required to fly the pattern. Passing approximately over the departure end of Runway XYR at approximately 400 ft. AGL [received priority] in order to deviate from ATC instructions and minimize the time in flight due to concerns of engine failure; informed ATC of intentions to land on Runway XX. ATC promptly provided landing clearance for any runway. Maneuvered to line up with Runway XX while maintaining appropriate safe airspeed using partial engine power. Quick check for landing gear down and added landing flaps. Landed normally approximately midfield Runway XX; comfortably taxied off on [Taxiway] 1. Informed ATC of intentions to taxi back to parking; but observed zero oil pressure during after-landing checklist and detected odor of burning oil. Stopped the aircraft in the non-movement area directly ahead of [Taxiway] 1 shut down the aircraft and evacuated. After evacuation observed the engine cowling; bottom of fuselage and some of the wing surfaces coated in engine oil. No fire occurred; no injury to persons on board or on the ground; no damage to airport structures. Successful outcome can be partially attributed to detailed pre-takeoff safety briefing including actions in case of engine failure and intended emergency runway to be used. Additionally; continuous and careful monitoring of instruments and engine gauges during critical phase of flight allowed for rapid detection of engine irregularities.