This research paper investigates Mobile Edge Computing (MEC) networks, which involve numerous wireless devices transferring their computation tasks to various edge servers and a single cloud server. The study considers various real-time dependent computation tasks composing an application running on each connected device. This study aims to determine whether to process each user task locally on the device or to offload and process it on one of the nearby MEC servers or the central cloud server. Despite the continued efforts to address the issue of task offloading, it remains a difficult area of research, especially in the edge-cloud environment. Improving the Quality of Service (QoS) and achieving optimized performance and resource utilization are still necessary goals. New approaches either focus on a single objective, are computationally demanding, depend only on the cloud or MEC for offloading, not both or disregard the interdependence between tasks. This paper proposes an enhanced multi-objective version of the Gorilla Algorithm (EMGA) for offloading interdependent tasks in edge-cloud environments, with three main objectives: 1-reducing the application's execution latency, 2-lowering energy consumption for connected devices, and 3-minimizing imposed cost for using servers' resources. The proposed approach assumes that each MEC and cloud server can support multiple cost levels to increase system flexibility. A customized mutation operation was introduced in EMGA, which extends the functionality of the Standard Gorilla algorithm to improve search strategies. Comparative analyses were conducted between EMGA and other optimizers in the problem domain, and the results indicate the superiority of EMGA.