Agile quadrotor avoidance of fast-moving obstacles requires anticipating collisions and selecting feasible maneuvers within short reaction windows. Reliable predictive avoidance remains challenging because sparse range observations do not directly reveal obstacle motion, while online trajectory optimizers either scale poorly with obstacle count or remain efficient at the expense of reliability in dense, high-speed encounters. We present OmniRisk, an omnidirectional planning framework that learns trajectory-level risk offline for efficient onboard evasion. A fixed-dimensional tensor combines LiDAR range panoramas, dynamic masks, and Cartesian surface velocities to represent geometry and motion jointly. We formulate an asymmetric risk field aligned with obstacle velocity that emphasizes approaching interactions and attenuates receding ones. Accumulating this risk along predicted relative trajectories provides dense supervision and discourages unnecessary hesitation after obstacles pass. A dual-branch circular convolutional network predicts terminal boundary states and dynamic risks for candidate primitives over an omnidirectional anchor lattice in a single forward pass, followed by selection and closed-form reconstruction of the selected candidate primitive. This formulation removes online risk accumulation along trajectories and makes risk-inference cost independent of obstacle count. OmniRisk enables efficient onboard avoidance, with real-world flights demonstrating consecutive evasive maneuvers at relative encounter speeds up to 15 m/s without fine-tuning. Code is available at https://github.com/VANdexj/OmniRisk.

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