Mobile edge computing (MEC) is emerging as a cornerstone technology to address the conflict between resource-constrained smart devices (SDs) and the ever-increasing computational demands of the mobile applications. MEC enables the SDs to offload computational-intensive tasks to the nearby edge nodes for providing better quality-of-services (QoS). The recently proposed offloading strategies, mainly consider a centralized approach for a limited number of SDs. However, with the growing popularity of the SDs, these offloading models may have the scalability issue and can be susceptible to single point failure. Although there are few distributed offloading models in the literature, they ignore the vast computational resources of the cloud, load sharing between the MEC servers, and other optimization parameters. Toward this end, we propose an efficient computation offloading scheme for a distributed load sharing MEC network in cooperation with cloud computing to enhance the capabilities of the SDs. We formulate a nonlinear multiobjective optimization problem by applying queuing theory to model the execution delay, energy consumption, and payment cost for using edge and cloud services. To solve the formulated problem, we propose a stochastic gradient descent (SGD) algorithm based solution approach to jointly optimize the offloading probability and transmission power of the SDs for finding an optimal trade-off between energy consumption, execution delay, and cost of the SDs. Finally, we perform extensive simulations to demonstrate the effectiveness of the proposed offloading scheme. Moreover, compared to the other solutions, the proposed scheme is scalable and outperforms the existing schemes.