To analyze the channel characteristics in omnidirectional reception scenarios for non-line-of-sight ultraviolet (UV) communication, we derive expressions for the reception direction distribution based on the incident photons at the receiver and propose an omnidirectional reception path loss (PL) channel model based on the Monte Carlo (MC) method. Furthermore, we validate the proposed omnidirectional model by comparing it with the existing MC numerical model that traverses all reception directions. Results indicate that the average computation time of the proposed omnidirectional PL model is less than 0.03% of the traversal model while maintaining comparable accuracy. Additionally, we present the variations in off-axis and inclination angles corresponding to the receiver's direction at different coordinate positions. Therefore, this paper provides valuable guidance for rapidly determining the omnidirectional energy field distribution and optimizing receiver orientation in UV communication systems.