To address the challenge of precise, dynamic and versatile aerial manipulation, we present an aerial manipulation platform consisting of a parallel 3-DOF manipulator mounted to an omnidirectional tilt-rotor aerial vehicle. The general modeling of a parallel manipulator on an omnidirectional floating base is presented, which motivates the optimization and detailed design of the aerial manipulator parameters and components. Inverse kinematic control of the manipulator is coupled to the omnidirectional base pose controller with a dynamic compensation term, going beyond common decoupled approaches. This presents a baseline for the control of redundant omnidirectional aerial manipulators. Experimental flights show the advantages of an active manipulator vs. a fixed arm for disturbance rejection and end effector tracking performance, as well as the practical limitations of the dynamic compensation term for fast end effector trajectories. The results motivate future studies for precise and dynamic aerial manipulation.