Driven by the explosive growth in computation-intensive applications in future 5G networks and industries, mobile edge computing (MEC), which enables smart terminals (STs) to offload their computation workloads to nearby edge servers (ESs) in radio access networks, has attracted increasing attention. In this article, we investigate the energy-efficient multitask multiaccess MEC via nonorthogonal multiple access (NOMA). Exploiting NOMA, an ST with multiple tasks can offload the respective computation workloads of different tasks to different ESs simultaneously. To study this problem, we adopt a two-step approach. Specifically, we first consider a given task-ES assignment and formulate a joint optimization of the tasks' computation offloading, local computation-resource allocation, and the NOMA-transmission duration, with the objective of minimizing the ST's total energy consumption for completing all tasks. Next, based on the optimal offloading solution for the given task-ES assignment, we further investigate how to properly assign different tasks to the ESs for further minimizing the ST's total energy consumption. For both the formulated problems, we propose efficient algorithms to compute the respective solutions. Numerical results are provided to validate the effectiveness of our proposed algorithms. The results also show that our proposed NOMA-enabled multitask multiaccess computation offloading can outperform conventional orthogonal multiple access based offloading scheme, especially when the tasks have heavy computation-workload requirements and stringent delay limits.