Mobile-edge computing (MEC) has recently emerged as a cost-effective paradigm to enhance the computing capability of hardware-constrained wireless devices (WDs). In this paper, we first consider a two-user MEC network, where each WD has a sequence of tasks to execute. In particular, we consider task dependency between the two WDs, where the input of a task at one WD requires the final task output at the other WD. Under the considered task-dependency model, we study the optimal task offloading policy and resource allocation (e.g., on offloading transmit power and local CPU frequencies) that minimize the weighted sum of the WDs' energy consumption and task execution time. The problem is challenging due to the combinatorial nature of the offloading decisions among all tasks and the strong coupling with resource allocation. To tackle this problem, we first assume that the offloading decisions are given and derive the closed-form expressions of the optimal offloading transmit power and local CPU frequencies. Then, an efficient bi-section search method is proposed to obtain the optimal solutions. Furthermore, we prove that the optimal offloading decisions follow an one-climb policy, based on which a reduced-complexity Gibbs Sampling algorithm is proposed to obtain the optimal offloading decisions. We then extend the investigation to a general multi-user scenario, where the input of a task at one WD requires the final task outputs from multiple other WDs. Numerical results show that the proposed method can significantly outperform the other representative benchmarks and efficiently achieve low complexity with respect to the call graph size.