Limbless robots have the potential to locomote through confined spaces but turning effectively within unmodelled and unsensed environments remains challenging. Nematode worms like C. elegans use a turning strategy dubbed the "omega turn"; we posited that such turns would yield benefits in limbless robots. Study of the dynamics of the worm's turns reveals a sequence of entry, reversal, and exit phases and a superposition of two traveling waves. We use geometric mechanics tools to model the superposition of two traveling waves to generate effective body rotation while avoiding self-collision, and generate a scheme to reorient the robot to arbitrary angles via modulation of joint angle amplitudes. We experimentally test the omega turn on a one-meter-long limbless 16-segment robot on hard ground, validating that the omega turn gait outperforms previous turning gaits: it results in a larger angular displacement and a smaller area swept by the body over a gait cycle, allowing the robot to turn in highly confined spaces. Through robot experiment, we demonstrate that the joint angle amplitude modulation scheme allows the robot to reorient to arbitrary angles between 35 and 98 degrees in one gait cycle.