In recent years, multimodal locomotion capabilities have enabled robots to maneuver in both terrestrial and aerial domains. However, most of these robots are designed only for locomotion, and few possess the manipulation capabilities required for practical tasks. By adding a manipulator, ground robots can perform manipulation, and some drones with robotic arms have demonstrated aerial manipulation. Nonetheless, such multirotors cannot be directly used for manipulation on the ground, and this configuration itself is unsuitable for air-ground hybrid locomotion. This is because their thruster-centralized structure makes it difficult to achieve both sufficient degrees of freedom (DoF) for manipulation and stable motion with contact and transformation. Therefore, in this work, we develop a new multilink multirotor with thrusters on each link and capable of contact with the environments. This robot can perform terrestrial rolling locomotion, aerial flight locomotion, and manipulation in multiple environments using joint actuation. First, we introduce a minimal configuration design of the proposed robot. We also describe a kinematic model and propose a design for each component based on this model. Second, we propose a real-time control method based on nonlinear optimization that considers contact and joint motion, which can be applied to various multirotors. Third, we propose motion strategies that include contact constraints specific to air-ground hybrid multilink multirotors, and analyze the limitations of manipulation capabilities based on multi-contact model. Finally, we demonstrate a variety of motions in both domains using the implemented prototype. To the best of our knowledge, this is the first demonstration of air-ground hybrid locomotion and manipulation by a multilink multirotor.