Power extraction from wind and water streams using flapping wings is known to be an alternative method to harvest renewable energy. The vortical flow structures around and in the wake of a NACA0012 airfoil oscillating with non-sinusoidal pitching and plunging motions are investigated using Digital Particle Image Velocimetry (DPIV) and compared with Navier-Stokes computations to give insight into the physics that determine the performance of an oscillating-wing power generator. A plunge amplitude of 1.05 chords, reduced frequency 0.8, pitch amplitude 73°, pivot point at quarter-chord and mid-chord, phase angles of 90° and 110°, and stroke reversal times ΔTR of 0.1 (rapid reversal) to 0.5 (sinusoidal) are used. It is shown that the vorticity formations are independent of the Reynolds number for the investigated cases (Re = 1100 - 1960). As the airfoil rotation speed during pitch reversals is increased, vortex shedding occurs earlier with higher strength. As the phase angle by which the pitching motion leads the plunging motions is increased, the shed vortex convection distance is also increased. Peak power coefficient (0.86) and efficiency (33%) are found at ΔTR = 0.3 for mid-chord pivot, with values of power coefficient (0.89) and efficiency (31%) at ΔTR = 0.5 for quarter-chord pivot. The leading edge vortex interaction with the airfoil and the timing of its formation and convection has the primary role in the time averaged power output.