This paper designs a helper-assisted resource allocation strategy in non-orthogonal multiple access (NOMA)-enabled mobile edge computing (MEC) systems, in order to guarantee the quality of service (QoS) of the energy/delay-sensitive user equipments (UEs). To achieve a tradeoff between the energy consumption and the delay, we introduce a novel performance metric, called \emph{energy-delay tradeoff}, which is defined as the weighted sum of energy consumption and delay. The joint optimization of user association, resource block (RB) assignment, power allocation, task assignment, and computation resource allocation is formulated as a mixed-integer nonlinear programming problem with the aim of minimizing the maximal energy-delay tradeoff. Due to the non-convexity of the formulated problem with coupled and 0-1 variables, this problem cannot be directly solved with polynomial complexity. To tackle this challenge, we first decouple the formulated problem into a power allocation, task assignment and computation resource allocation (PATACRA) subproblem. Then, with the solution obtained from the PATACRA subproblem, we equivalently reformulate the original problem as a discrete user association and RB assignment (DUARA) problem. For the PATACRA subproblem, an iterative parametric convex approximation (IPCA) algorithm is proposed. Then, based on the solution obtained from the PATACRA subproblem, we first model the DUARA problem as a four-sided matching problem, and then propose a low-complexity four-sided UE-RB-helper-server matching (FS-URHSM) algorithm. Theoretical analysis demonstrates that the proposed algorithms are guaranteed to converge to stable solutions with polynomial complexity. Finally, simulation results are provided to show the superior performance of our proposed algorithm in terms of the energy consumption and the delay.