Omnidirectional MAVs are a growing field, with demonstrated advantages for aerial interaction and uninhibited observation. While systems with complete pose omnidirectionality and high hover efficiency have been developed independently, a robust system that combines the two has not been demonstrated to date. This paper presents VoliroX: a novel omnidirectional vehicle that can exert a wrench in any orientation while maintaining efficient flight configurations. The system design is presented, and a 6 DOF geometric control that is robust to singularities. Flight experiments further demonstrate and verify its capabilities.