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Incorporating mobile edge computing (MEC) in Internet of Things (IoT) enables resource-limited IoT devices to offload their computation tasks to a nearby edge server. In this paper, we investigate an IoT system assisted by the MEC technique with its computation task subjected to sequential task dependency, which is critical for video stream processing and other intelligent applications. To minimize energy consumption per IoT device while limiting task processing delay, task offloading strategy, communication resource, and computation resource are optimized jointly under both slow and fast fading channels. In slow fading channels, an optimization problem is formulated, which is non-convex and involves one integer variable. To solve this challenging problem, we decompose it as a one-dimensional search of task offloading decision problem and a non-convex optimization problem with task offloading decision given. Through mathematical manipulations, the non-convex problem is transformed to be a convex one, which is shown to be solvable only with the simple Golden search method. In fast fading channels, optimal online policies depending on instant channel state are derived even though they are entangled. In addition, it is proved that the derived policy will converge to the offline policy when channel coherence time is low, which can help to save extra computation complexity. Numerical results verify the correctness of our analysis and the effectiveness of our proposed strategies over existing methods.