Micro aerial vehicles, such as multirotors, are particular well suited for the autonomous exploration, examination, and surveillance of otherwise inaccessible areas, e.g., for search and rescue missions in indoor disaster sites. Key prerequisites for the fully autonomous operation of micro aerial vehicles in restricted environments are 3D mapping, real-time pose tracking, obstacle detection, and planning of collision-free trajectories. In this work, we propose a complete navigation system with a multimodal sensor setup for omnidirectional environment perception. Measurements of a 3D laser scanner are aggregated in egocentric local multiresolution grid maps. Local maps are registered and merged to allocentric maps in which the MAV localizes. For autonomous navigation, we generate trajectories in a multi-layered approach: from mission planning over global and local trajectory planning to reactive obstacle avoidance. We evaluate our approach in a GNSS-denied indoor environment where multiple collision hazards require reliable omnidirectional perception and quick navigation reactions.