With the exponential growth of maritime wireless devices and the rapid development of maritime applications, traditional maritime communication networks encounter communication and computation limitations in supporting computation-intensive and latency-critical tasks. Edge computing and Intelligent Reflecting Surface (IRS) have emerged as promising techniques to improve communication and computation services for maritime devices with limited computation capabilities and battery capacity. This paper studies an IRS Mounted on Unmanned Aerial Vehicle (UIRS) assisted maritime edge computing network, in which the UIRS is deployed to assist the transmission from Unmanned Surface Vehicles (USVs) to the edge server via Non-Orthogonal Multiple Access (NOMA) protocol. We propose a resource management and trajectory optimization scheme by jointly optimizing subslot duration, offloading ratios, transmit power, edge computation capability allocation, UIRS phase shifts and UIRS trajectory, aiming at minimizing the overall energy consumption. Since the non-convex nature of the optimization problem, we propose a two-layered method by decomposing the original problem into two subproblems. The top-layered subproblem is solved by the Semi-Definite Relaxation (SDR) method and the underlying-layered subproblem is solved by the Deep Deterministic Policy Gradient (DDPG) algorithm. Numerical results demonstrate that our proposed scheme can effectively and efficiently reduce overall energy consumption.