As the number of unmanned aerial vehicles (UAVs) and computational tasks increases in UAV Ad-hoc Network (UAVANETs), the solution space for task allocation strategies grows exponentially. In practical multi-user concurrent emergency scenarios, multi-UAV systems equipped with mobile edge computing (MEC) devices face challenges such as dynamic network topologies and uneven task allocation. To address these issues, we propose an adaptive task allocation strategy, AUSTA-DQHO, which integrates the deep Q-network (DQN) algorithm with genetic algorithms. In our approach, the random action selection process in DQN is replaced with a genetic mechanism, enabling more efficient decision-making for the optimal task allocation for each offloading request through iterative optimization. Under the multi-UAV-assisted MEC network architecture, AUSTA-DQHO optimizes computational task scheduling to minimize the total mission time, from the UAVs’ departure from the base station to the completion of all tasks. To accelerate the convergence of the AUSTA-DQHO strategy while ensuring global optimal solutions, we introduce a pre-clustering mechanism and weighting factor for randomly generated task offloading requests in the target area, effectively reducing the solution space. Experimental results demonstrate that AUSTA-DQHO outperforms traditional DQN-based strategies in terms of faster learning capabilities and greater robustness. Furthermore, we explore the optimal number of UAVs under specific environmental conditions to minimize the waste of computational resources.