Mobile edge computing (MEC) is an essential technique in next-generation networks to serve ultra-low latency and computation-intensity applications. At the same time, nonorthogonal multiple access (NOMA) is a technique to help multi-user service, saving energy and increasing spectrum efficiency. In this study, we investigate the NOMA MEC-based wireless Tactile Internet of Things (IoT) network and propose the optimization algorithms for system and users performance: We propose a network model consisting of a MEC server at the access point that supports computation for two sensor clusters in the Tactile IoT environment. We analyze the performance of the system and cluster heads (CHs) using the successful computation probability (SCP). Asymptotic SCP at high SNRs was analyzed and compared by us to give a better view of the system's behavior. Then, we maximize the SCP of the proposed system and simultaneously maximize the SCP of the CHs to clarify the performance trade-off problem in the NOMA MEC network by proposing low-complexity meta-heuristic algorithms. Monte-Carlo simulation results show that our proposed approach can significantly improve system performance by up to 30% compared to OMA traditional methods.