We propose a novel aerial manipulation platform, an omnidirectional aerial robot, that is capable of omnidirectional wrench generation with opportunistically distributed/aligned Sectional rotors. To circumvent the tight thrust margin and weight budget of currently available rotor and battery technologies, we propose a novel design optimization framework, which maximizes the minimumguaranteed control force/torque for any attitude while incorporating such important and useful aspects as interrotor aerointerference, anisotropic task requirement, gravity compensation, etc. We also provide a closed-form solution of infinity-norm optimal control allocation to avoid rotor saturation with the tight thrust margin. Further, we elaborate the notion of electronic speed controller induced singularity and devise a novel selective mapping algorithm to substantially subdue its destabilizing effect. Experiments are performed to validate the theory, which demonstrate such capabilities not possible with typical aerial manipulation systems, namely, separate translation and attitude control on SE(3), hybrid pose/wrench control with downward force of 60 N much larger than its own weight (2.6 kg), and peg-inhole teleoperation with a radial tolerance of 0.5 mm.