Internet of Things (IoT) tasks are offloaded to servers located at the edge network for improving the power consumption of IoT devices and the execution times of tasks. However, deploying edge servers could be difficult or even impossible in hostile terrain or emergency areas where the network is down. Therefore, edge servers are mounted on unmanned aerial vehicles (UAVs) to support task offloading in such scenarios. However, the challenge is that the UAV has limited energy, and IoT tasks are delay-sensitive. In this paper, a UAV-based offloading strategy is proposed where first, the IoT devices are dynamically clustered considering the limited energy of UAVs, and task delays, and second, the UAV hovers over each cluster head to process the offloaded tasks. The optimization problem of dynamically determining the optimal number of clusters, specifying the member tasks of each cluster, is modeled as a mixed-integer, nonlinear constraint optimization. A discrete differential evolution (DDE) algorithm with new mutation and crossover operators is proposed for the formulated optimization problem, and compared with the particle swarm optimization (PSO) and genetic algorithm (GA) meta-heuristics. Further, the ant colony optimization (ACO) algorithm is employed to identify the shortest path over the cluster heads for the UAV to traverse. The simulation results validate the effectiveness of the proposed offloading strategy in terms of tasks delays and UAV energy consumption.