Flight Instructor on training flight reported engine failure during takeoff climb.

Narrative

I was PIC (Pilot in Command) of Oxford that departed on an IFR flight plan off of Runway XXL at ZZZ destined for ZZZ1. 3 souls on board - myself in the right pilot seat; Student Pilot 1 in the left pilot seat; and Student Pilot 2 in the left rear seat. After receiving takeoff clearance; SP (Student Pilot) 1 performed a normal takeoff with all engine indications appearing normal. At around 1900 ft. MSL on the upwind; we felt and heard something abnormal; and I quickly noticed our engine power decaying. The stall horn began to sound. I took control of the aircraft; lowered the nose; and confirmed that we were at full throttle; full mixture; mags on; fuel pump on. The engine power was hovering around 2100-2200 RPM max. After considering a suitable landing spot to the west of the field; I contacted Tower and stated my intention to return to the field; as I was still able to maintain altitude with partial power. Tower acknowledged and instructed left traffic Runway XXL. I repeated the instruction and began a shallow bank toward the downwind. As I turned through 180 degrees; I made the decision to return to land on the opposite runway; Runway XXR; as I was unsure of the severity of the issue or if I would have enough engine power to make it back to Runway XXL. I immediately informed ATC of my intentions and they were quick to acknowledge and clear all traffic from the runway. Once I had the runway made; I deployed full flaps; landed on XXR; and taxied to the ramp under my own power. Upon exiting the aircraft; we noticed a significant amount of oil smeared across the side of the engine cowling.