Omnidirectional micro aerial vehicles are a growing field of research, 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 the design and optimal control of a novel omnidirectional vehicle that can exert a wrench in any orientation while maintaining efficient flight configurations. The system design is motivated by the result of a morphology design optimization. A six degrees of freedom optimal controller is derived, with an actuator allocation approach that implements task prioritization, and is robust to singularities. Flight experiments demonstrate and verify the system's capabilities.