The rapid expansion of mobile edge computing (MEC), driven by the escalating data volume and the demand for minimal network latency, underscores the need for efficient data processing. To address the growing complexity of neural networks and applications, segmentation into smaller components (e.g., neural network layers, subnetworks, and subtasks) for parallel computation across diverse nodes is common. However, effective data transmission between these segments necessitates optimized task scheduling among edge servers. Many platforms leverage container-based operating system-level virtualization to enhance edge computing efficiency, leveraging container image layers to cut storage and transmission costs. However, previous research predominantly emphasizes task scheduling, overlooking runtime environment preparation on edge servers and potential collaboration among edge nodes. This article introduces an innovative approach that adeptly manages task data and image layer dependencies collaboratively. It formulates an NP-hard problem: minimizing total computation completion time by jointly determining downlink transmission rate allocation, task-offloading strategies, and layer-loading schemes, allowing for thoughtful decoupling and iterative refinement. The Gray Wolf Optimizer and cellular automata are introduced for dynamic task scheduling, complemented by a low-complexity algorithm inspired by the Nawas-Enscore-Ham method. For layer downloading, this article explores a partial-layer loading policy, considering storage constraints, and establishes a full-layer loading strategy with the Peer-to-Peer mechanism, significantly reducing computational complexity. Rigorous experimental results underscore the remarkable efficacy of these approaches in curtailing total computation completion time, positioning them as benchmarks for comparison against alternative solutions.