Traditional aerial vehicles are constrained to perform specific tasks due to their adhoc designs. Based on modularity, we propose a versatile robot, H-ModQuad, that can adapt to different tasks by increasing its load capacity and actuated degrees of freedom. It is composed of cuboid modules propelled by quadrotors with tilted rotors. We present two families of module designs that bring scalable and versatile actuation to the aerial systems. By configuring multiple modules, H-ModQuad can increase its payload capacity and change its actuated degrees of freedom from 4 to 5 and 6. By modeling the actuation capability of H-ModQuad using actuation ellipsoids and wrench polytopes, we find the body frame of a vehicle that maximizes its thrusting efficiency. We also compare the vehicle capabilities against formally defined task requirements. We present the dynamics of H-ModQuad and integrate control strategies despite the vehicle design. The design and model are validated with experiments using actual robots, showing that H-ModQuad vehicles with different configurations provide different actuation properties.