Mobile edge computing (MEC) supported by non-orthogonal multiple access (NOMA) has recently gained a lot of interest due to its improved ability to lessen power consumption and MEC offload delay. In recent decades, the need for wireless communications has increased tremendously. Fifth-generation (5G) communications will soon be widely used and offer much more functionality than a fourth generation (4G). Between 2027 and 2030, an innovative wireless communication paradigm is known as the sixth generation (6G) system is projected to be introduced with the full help of artificial intelligence (AI). Advanced system capacity, higher data rate, lower latency, advanced security, and improved quality of service (QoS) than 5G systems are a few of the main challenges to resolve with 5G. The growing need for data rates in the sixth generation (6G) communication networks are being met by extraordinary technologies such as NOMA, Soft Computing (SC), and MEC. Owing to the massive attention to the NOMA-enabled MEC, there has been a significant spike in the number of papers published in this area, while more comprehensive studies and classifications are still needed. Using the preferred reporting items for systematic reviews and meta-analysis (PRISMA) guidelines, the investigation reports a systematic literature review (SLR) of NOMA-enabled MEC. This survey also evaluates numerous pieces of literature prudently chosen over a multi-step procedure and meets the selection criteria described in the paper summarizing our review.