<p>Cloud computing delivers real-time customizable capabilities and functionalities over the Internet, thereby revolutionizing the computing industry. Task scheduling in the cloud model has attracted the researchers’ interest owing to its complexity, heterogeneity, and dynamic properties because tasks vary in size and processing capacity. Consequently, poor scheduling techniques can lead to higher energy usage and service level agreements (SLAs). The literature on task scheduling has mainly dealt with designing and developing scheduling algorithms rather than examining how uncertain factors, such as network bandwidth and instruction rate, affect scheduling. This study proposes a novel task scheduling method using the Osprey Optimization Algorithm (OOA) by examining the impact of the network capacity and instruction rate. To further enhance the search capabilities of the classic OOA and address challenges such as sluggish convergence and local optimum behavior, the OOA is modified with novel methods, namely, Roulette fitness-distance-balance-based (RFDB) selection, Brownian movement, and Lévy flight. Brownian movement and Lévy flight strategies improve exploration capabilities, whereas RFDB ensures a balanced search for global optimal solutions. The simulation results demonstrated that EOOA achieved significant improvements, reducing the makespan by 27%, energy consumption by 36%, and SLA violations by 50% compared to baseline algorithms, highlighting its superior performance in task scheduling across diverse workloads.</p>