The past decades have witnessed an explosive growth of the Internet of Things (IoT) services requiring intensive computation resources. The conventional IoT devices, however, are usually equipped with very limited computation resources, which results in degraded quality of experience when executing the resource-hungry applications. Mobile edge computing (MEC), which enables smart terminals (STs) to offload parts of their computation workloads to the edge servers located at cellular base stations (BSs), has provided a promising approach to address this issue. In this article, we investigate the nonorthogonal multiple access (NOMA)-enabled multiaccess MEC. Specifically, by exploiting the advanced NOMA, an ST can simultaneously offload its computation workloads to different edge servers (ESs), which thus reduces the overall delay in completing the ST's computation workloads. To study this problem, we formulate a joint optimization of the computation resource allocations at the ESs, the ST's offloaded workloads and its radio resource allocations for NOMA transmission, with the objective of minimizing a system wise cost that accounts for the overall delay in finishing the ST's total computation workload and the total computation resource usage cost at the ESs. Despite the nonconvexity of the joint optimization problem, we exploit its layered structure and propose an efficient layered algorithm to find the optimal solution. By exploiting the optimal offloading solution of a single ST, we further investigate the scenario of multiple STs and propose two algorithms to determine the optimal grouping among different ESs for serving the STs, with one algorithm aiming at minimizing the total cost of all STs and the other algorithm aiming at determining the Nash stable grouping for the ESs. Numerical results are presented to validate the effectiveness of our proposed algorithms and show the performance gain of our proposed NOMA-enabled multiaccess computation offloading.