Device-to-device (D2D)-assisted mobile edge computing (MEC) is one of the critical technologies of future sixth generation (6G) networks. The core of D2D-assisted MEC is to reduce system latency for network edge UEs by supporting cloud computing services, thereby achieving high-speed transmission. Due to the sensitivity of communication signals to obstacles, relaying is adopted to enhance the D2D-assisted MEC system's performance and its coverage area. However, relay nodes and the base station (BS) are typically equipped with large-scale antenna arrays. This increases the cost of relay-assisted D2D MEC systems and limits their deployment. Movable antenna (MA) technology is used to work around this limitation without compromising performance. Specifically, the core of MA technology lies in optimizing the antenna positions to increase system capacity. Therefore, this paper proposes a novel resource allocation scheme for MA-enhanced relay-assisted D2D MEC systems. Specifically, the MA positions and beamforming of user equipments (UEs), relay, and BS as well as the allocation of resources and the computation task offloading rate at the MEC server, all are optimized herein with the objective of minimizing the maximum latency while satisfying computation and communication rate constraints. Since this is a multivariable non-convex problem, a parallel and distributed penalty dual decomposition (PDD) based algorithm is developed and combined with successive convex approximation (SCA) to solve this non-convex problem. The results of extensive numerical analyses show that the proposed algorithm significantly improves the performance of the MA-enhanced relay-assisted D2D communication system compared to a counterpart where relays and the BS are equiped with traditional fixed-position antenna (FPA).