The integration of unmanned aerial vehicles (UAVs) and marine communication networks has been emerging as a promising paradigm to cater for the growing maritime activities, e.g., marine environment monitoring and ocean resource exploration. The increasing growth of marine applications and services poses challenges for processing marine data, while the resources-limited UAVs cannot satisfy the requirements of computing-intensive and energy consumption. In this paper, we consider a marine edge computing scenario with a group of UAVs and ocean beacon stations (OBSs) and propose a multi-UAV aided multi-access edge computing for marine networks from the perspective of system-welfare and energy-efficient design. Specifically, we propose a multi-task multi-access offloading scheme in marine edge computing networks, in which multiple UAVs can process their workloads locally or offload their partial workloads to multiple OBSs for processing. We consider the total utilities for completing all tasks as the system welfare, and measure the difference between the system welfare and energy consumption as the system revenue. A joint optimization problem is formulated by optimizing the OBS selection, the offloading ratio and the transmission duration, with the objective of increasing the system revenue in marine edge computing networks. We exploit a vertical decomposition architecture to solve the formulated non-convex problem via decomposing it into three sub-problems. Regarding each sub-problem, we propose efficient algorithms to derive the optimal solutions. We finally conduct simulations to verify the performance of the proposed algorithms. The results demonstrate that our proposed algorithms can achieve the best performance for improving the system revenue in comparison with several benchmark algorithms.