Starting current depends on the kind of motor (and its load, etc.) If it's a shaded pole induction motor, which would be my guess, it's probably not too much different than the operating current. Do note that the power factor could be somewhat poor, so the 120W motor could consume more than 120 VA.
How well the motor functions on a non-sinusoidal power input also varies with the kind of motor. An induction motor typically will have somewhat lower torque (and hence speed) and run somewhat less efficiently (warmer), but not unreasonably so unless it's sized very marginally for its task or run for very long periods of time (or both). A universal motor with brushes will be relatively little affected by the differing waveforms.
BFL's suspicion that the inverter is shutting down from undervoltage at its input rather than overcurrent at its output has merit. I think most inverters—at least inexpensive ones—are mainly protected from excess power draw by the DC input fuses. I may well be wrong.