Flying manipulators are aerial drones with attached rigid-bodied robotic arms and belong to the latest and most actively developed research areas in robotics. The rigid nature of these arms often lack compliance, flexibility, and smoothness in movement. This work proposes to use a soft-bodied robotic arm attached to an omnidirectional micro aerial vehicle (OMAV) to leverage the compliant and flexible behavior of the arm, while remaining maneuverable and dynamic thanks to the omnidirectional drone as the floating base. The unification of the arm with the drone poses challenges in the modeling and control of such a combined platform; these challenges are addressed with this work. We propose a unified model for the flying manipulator based on three modeling principles: the Piecewise Constant Curvature (PCC) and Augmented Rigid Body Model (ARBM) hypotheses for modeling soft continuum robots and a floating-base approach borrowed from the traditional rigid-body robotics literature. To demonstrate the validity and usefulness of this parametrisation, a hierarchical model-based feedback controller is implemented. The controller is verified and evaluated in simulation on various dynamical tasks, where the nullspace motions, disturbance recovery, and trajectory tracking capabilities of the platform are examined and validated. The soft flying manipulator platform could open new application fields in aerial construction, goods delivery, human assistance, maintenance, and warehouse automation.