Unmanned aerial vehicle (UAV) has received tremendous attention in the area of edge computing due to its flexible deployment and wide coverage accessibility. In weak infrastructure scenarios, multiple UAVs can form on-site edge computing clusters to handle the real-time tasks. Further, a multi-UAV enabled edge-cloud computing system is coined by cooperating the UAVs with remote cloud, which provides superior computing capability. However, the uneven distribution of tasks makes it difficult to meet the real-time requirements when load balancing is unavailable. To address above issue, a delay minimization problem for multi-UAV enabled edge-cloud cooperative offloading is investigated in this paper. The problem is formulated as a non-convex problem based on models that reflect characteristics of the system, such as ubiquitous network congestion, air-to-ground wireless channel and cooperative parallel computing. An efficient cooperative offloading algorithm is proposed to address the problem. Specifically, convex approximation is applied to make the original problem tractable, and Lyapunov optimization is utilized to make online task offloading decisions. Finally, the correctness of the models are verified through a practical UAV-edge computing platform. Simulations based on measurement results and real-world datasets indicate that, the proposed algorithm fully utilizes the available energy to significantly reduce the tasks' completion delay.