Mobile-edge computing (MEC) is considered as a promising technology to reduce the energy consumption (EC) and task accomplishment latency of smart mobile user equipments (UEs) by offloading computation-intensive tasks to the nearby MEC servers. However, the Quality of Experience (QoE) for computation highly depends on the wireless channel conditions when computation tasks are offloaded to MEC servers. In this article, by considering the imperfect channel-state information (CSI), we study the joint offloading decision, transmit power, and computation resources to minimize the weighted sum of EC of all UEs while guaranteeing the probabilistic constraint in multiuser MEC-enabled Internet-of-Things (IoT) networks. This formulated optimization problem is a stochastic mixed-integer nonconvex problem and challenging to solve. To deal with it, we develop a low-complexity two-stage algorithm. In the first stage, we solve the relaxed version of the original problem to obtain offloading priorities of all UEs. In the second stage, we solve an iterative optimization problem to obtain a suboptimal offloading decision. As both stages include solving a series of nonconvex stochastic problems, we present a constrained stochastic successive convex approximation-based algorithm to obtain a near-optimal solution with low complexity. The numerical results demonstrate that the proposed algorithm provides comparable performance to existing approaches.