With the rapid development of Internet of Things (IoT) technology, Terminal Devices (TDs) are more inclined to offload computing tasks to higher-performance computing servers, thereby solving the problems of insufficient computing capacity and rapid battery consumption of TD. The emergence of Multi-access Edge Computing (MEC) technology provides new opportunities for IoT task offloading. It allows TDs to access computing networks through multiple communication technologies and supports more mobility of terminal devices. Review studies on IoT task offloading and MEC have been extensive, but none of them focus on IoT task offloading in MEC. To fill this gap, this paper provides a comprehensive and in-depth understanding of the algorithms and mechanisms of multiple IoT task offloading in the MEC network. For each paper, the main problems solved by the mechanism, technical classification, evaluation methods, and supported parameters are extracted and analyzed. Furthermore, shortcomings of current research and future research trends are discussed. This review will help potential and new researchers quickly understand the panorama of IoT task offloading approaches in MEC and find appropriate research paths.