With the rapid increase in the use of cloud computing systems, an efficient task scheduling policy, which deals with the assignment of tasks to resources, is required to obtain maximum performance. Cloud task scheduling (CTS) is an established NP-Hard optimization problem that can be effectively tackled with meta-heuristic algorithms. The cuckoo search (CS) algorithm is a powerful swarm-intelligence meta-heuristic that has been successfully applied over a wide-range of real-life optimization problems, including task scheduling problems. Besides its strong exploration ability, the CS algorithm suffers from insufficient local search, lack of solution diversity towards the end, and slow convergence problem. These drawbacks produce inefficient cloud task schedules resulting in sub-optimal performance. In this manuscript, an improved CS-based scheduling algorithm called CSDEO is introduced, which combines the features of the Opposition-based learning (OBL) method, Cuckoo search, and Differential evolution (DE) algorithms to optimize workload makespan and energy consumption of the cloud resources. Our CSDEO algorithm firstly uses the OBL method to produce an optimal initial population by providing solutions across the entire solution space. Then, the CSDEO uses an effective way of switching between the CS exploration phase and the DE exploitation phase, depending on each solution's fitness. Experiments are conducted on the CloudSim simulator by using the CEA-Curie and HPC2N supercomputing workloads. The observations show that in the case of CEA-Curie workloads, the proposed CSDEO algorithm achieves makespan improvement in the range of 6.29-29.76% and energy consumption improvement in the range of 3.76-201.98% over well-known scheduling algorithms. In the case of HPC2N workloads, the improvement ranges of the CSDEO approach for the makespan and energy consumption metrics are 9.86-281.69% and 6.12-233.3%, respectively compared to the tested scheduling algorithms.