The decentralized state estimation is one of the most fundamental components for autonomous aerial swarm systems in GPS-denied areas, which still remains a highly challenging research topic. To address this research niche, the Omni-swarm, a decentralized omnidirectional visual-inertial-UWB state estimation system for the aerial swarm is proposed in this paper. In order to solve the issues of observability, complicated initialization, insufficient accuracy and lack of global consistency, we introduce an omnidirectional perception system as the front-end of the Omni-swarm, consisting of omnidirectional sensors, which includes stereo fisheye cameras and ultra-wideband (UWB) sensors, and algorithms, which includes fisheye visual inertial odometry (VIO), multi-drone map-based localization and visual object detector. A graph-based optimization and forward propagation working as the back-end of the Omni-swarm to fuse the measurements from the front-end. According to the experiment result, the proposed decentralized state estimation method on the swarm system achieves centimeter-level relative state estimation accuracy while ensuring global consistency. Moreover, supported by the Omni-swarm, inter-drone collision avoidance can be accomplished in a whole decentralized scheme without any external device, demonstrating the potential of Omni-swarm to be the foundation of autonomous aerial swarm flights in different scenarios.