High-power autonomous soft actuators are in high demand yet face challenges related to tethered power and dedicated control. Light-driven oscillation by stimuli-responsive polymers allows for remote energy input and control autonomy, but generating high output power density is a daunting challenge requiring an advanced material design principle. Here, inspired by the flight muscle structure of insects, we develop a self-oscillator based on two antagonistically contracting photo-active layers sandwiching an inactive layer. The actuator produces an output power density of 33 W kg-1, 275-fold higher than other configurations and comparable to that of insects. Such oscillators allow for broad-wavelength operation and multifunction integration, including proprioceptive actuation and energy harvesting. We demonstrate high-performance flapping motion enabling various locomotion modes, including a wing with a thrust-to-weight ratio of 0.32. This work advances autonomous, sustained and untethered actuators for powerful robotics.