This paper presents a novel solution to the three-dimensional (3D) cooperative hunting of multiple drones that deals with surrounding a target simultaneously while navigating around obstacles in the cluttered dynamic 3D environment. Meanwhile, drones avoid the airflow downwash force created by the spinning propellers on unmanned aerial vehicles (UAVs) and their effect on the other UAVs. This solution consists of a 3D Simultaneous Encirclement strategy, the cooperative hunting objective with a novel revised particle swarm optimization (PSO*) path planning algorithm, a flocking theory-inspired obstacle avoidance algorithm, and a cascade PI controller. Simulation results with varying conditions were carried out to validate the effectiveness of the proposed solution by successfully taking care of the downwash effects, and having multiple hunter UAVs hunt and encircle a moving or stationary target in a dynamic or static obstacle-rich cluttered environment.