The offloading of computationally intensive tasks to edge servers is indispensable in the mobile edge computing (MEC) environment. Once the tasks are offloaded, the subsequent challenges lie in buffering them and assigning them to edge virtual machine (VM) resources to meet the multicriteria requirement. Furthermore, the edge resources’ availability is dynamic in nature and needs a joint prediction and optimal allocation for the efficient usage of resources and fulfillment of the tasks’ requirements. To this end, this work has three contributions. First, a delay sensitivity-based priority scheduling (DSPS) policy is presented to schedule the tasks as per their deadline. Secondly, based on exploratory data analysis and inferred seasonal patterns in the usage of edge CPU resources from the GWA-T-12 Bitbrains VM utilization dataset, the availability of VM resources is predicted by using a Holt−Winters-based univariate algorithm (HWVMR) and a vector autoregression-based multivariate algorithm (VARVMR). Finally, for optimal and fast task assignment, a parallel differential evolution-based task allocation (pDETA) strategy is proposed. The proposed algorithms are evaluated extensively with standard performance metrics, and the results show nearly 22%, 35%, and 69% improvements in cost and 41%, 52%, and 78% improvements in energy when compared with MTSS, DE, and min−min strategies, respectively.