<p>Recently, the current task-offloading strategies in edge-cloud systems face several significant challenges, primarily driven by the emerging need for computational resources in mobile applications. Furthermore, the existing system struggles to optimize complex, multi-objective constraints simultaneously, like minimizing makespan, controlling associated energy consumption and cost requirement, and ensuring robust security during the offloading process. These limitations motivate the developed approach for implementing effective task-offloading strategies within edge-cloud networks. This study seeks to improve task offloading by employing a Hybrid Walrus-Lemur Optimizer (H-WLO) approach to boost performance. The task offloading is executed using the introduced H-WLO. The HWLO aims to solve the application execution latency. The main aim correlated with this designed task-offloading model is to enhance the efficiency of task-offloading, along with the resource allocation in edge-cloud environments. This is accomplished by maximizing resource utilization, minimizing task rejection, and decreasing round-trip time to ensure timely completion of tasks within their deadlines. The multi-objective constraints for the implemented H-WLO-assisted energy aware task offloading system are resource utilization, makespan, cost, energy consumption, and security. The recommended H-WLO-based framework is designed to manage task offloading based on real-time conditions. The proposed H-WLO is comparing to the existing optimization to ensure the developed task allocation model’s efficacy regarding makespan, energy consumption, cost, etc. The findings showcased that the designed model enhances the throughput by 98.59&#xa0;Hz, which is higher than the other conventional approaches. The H-WLO-based task offloading strategy effectively tackles the challenges faced in edge-cloud networks, offering a scalable solution for upcoming mobile applications.</p>