In recent years, the Internet of Things (loT) and mobile communication technologies have developed rapidly. Meanwhile, many delay-sensitive and computation-intensive loT services have been widely applied. Because of the limited computing resources, storage, and battery capacity of lot devices, mobile edge computing (MEC) is emerging as a promising paradigm to help process the tasks of loT devices. Furthermore, non-orthogonal multiple access (NOMA) has evolved as a practical approach to meeting the requirement of massive connectivity. In this paper, we study the NOMA-aided dynamic task offloading problem for the loT, which combines task scheduling and computing resource allocation decisions. We model and formulate the problem as a stochastic optimization problem, and our goal is to minimize the system energy consumption while satisfying performance requirements. We transform the original problem into a deterministic optimization problem through stochastic optimization technology. Then, we decompose it into four sub-problems and propose the energy efficient task offloading (EETO) algorithm to solve these four sub-problems. Our proposed EETO algorithm does not rely on prior statistical knowledge related to task arrival or wireless channel conditions. Through theoretical analysis and experiment results, we demonstrate that our EETO algorithm can make a flexible trade-off between system energy consumption and performance. Additionally, the EETO algorithm can effectively decrease the system energy consumption while ensuring system performance.