Mobile edge computing (MEC) and terahertz (THz)enabled unmanned aerial vehicle (UAV) communication systems are gaining significant attention for improving user service delays in future mobile networks. This article introduces a novel multi-UAV-aided MEC system operating at THz frequencies to minimize expected user service delays, including communication and computation latency. We address this challenge by jointly optimizing UAV relay selection, power control, positioning, and user-resource association for task offloading and resource allocation. To tackle the problem's complexities, we decompose it into four subproblems, each solved optimally with our proposed algorithm. An iterative penalty dual decomposition (PDD) algorithm approximates the original problem's solution. Numerical results demonstrate that our PDD-based approach outperforms baseline algorithms in terms of expected user service delay.