Mobile edge computing (MEC) enables resource-limited IoT devices to complete computation-intensive or delay-sensitive task by offloading the task to adjacent edge server deployed at the base station (BS), thus becoming an important technology in 5G and beyond. Due to channel occlusion, some users may not be able to access the computation capability directly from the BS. Confronted with this issue, many other devices in the MEC system can serve as cooperative nodes to collect the tasks of these users and further forward them to the BS. In this paper, we study a MEC system in which multiple users continuously generate the tasks and offload the tasks to the BS through a cooperative node. As the tasks are continuously generated, users should simultaneously execute the task generation in the current time frame and the task offloading of the last time frame, i.e. the task is processed in a streaming model. To optimize the power consumption of the users and the cooperative node for finishing these streaming tasks, we investigate the duration of each step in finishing the tasks together with multiuser offloading ratio and bandwidth allocation within two cases: the BS has abundant computation capacity (Case I) and the BS has limited computation capacity (Case II). For both cases, the formulated optimization problems are nonconvex due to fractional structure of the objective function and complicated variable coupling. To address this issue, we propose optimal solution algorithm with low complexity. Finally, simulation is carried out to verify the effectiveness of the proposed methods and reveal the performance of the considered system.