Multiaccess mobile edge computing (MA-MEC) has been envisioned as one of the key approaches for enabling computation-intensive yet delay-sensitive services in future industrial Internet of Things (IoT). In this article, we exploit nonorthogonal multiple access (NOMA) for computation offloading in MA-MEC and propose a joint optimization of the multiaccess multitask computation offloading, NOMA transmission, and computation-resource allocation, with the objective of minimizing the total energy consumption of IoT device to complete its tasks subject to the required latency limit. We first focus on a static channel scenario and propose a distributed algorithm to solve the joint optimization problem by identifying the layered structure of the formulated nonconvex problem. Furthermore, we consider a dynamic channel scenario in which the channel power gains from the IoT device to the edge-computing servers are time varying. To tackle with the difficulty due to the huge number of different channel realizations in the dynamic scenario, we propose an online algorithm, which is based on deep reinforcement learning (DRL), to efficiently learn the near-optimal offloading solutions for the time-varying channel realizations. Numerical results are provided to validate our distributed algorithm for the static channel scenario and the DRL-based online algorithm for the dynamic channel scenario. We also demonstrate the advantage of the NOMA assisted multitask MA-MEC against conventional orthogonal multiple access scheme under both static and dynamic channels.