Stacked AutoEncoders (SAE) have been widely adopted in edge anomaly detection scenarios. However, the resource-intensive nature of SAE can pose significant challenges for edge devices, which are typically resource-constrained and must adapt rapidly to dynamic and changing conditions. Optimizing SAE to meet the heterogeneous demands of real-world deployment scenarios, including high performance under constrained storage, low power consumption, fast inference, and efficient model updates, remains a substantial challenge. To address this, we propose an integrated optimization framework that jointly considers these critical factors to achieve balanced and adaptive system-level optimization. Specifically, we formulate SAE optimization for edge anomaly detection as a multi-objective optimization problem and propose MO-SAE (Multi-Objective Stacked AutoEncoders). The multiple objectives are addressed by integrating model clipping, multi-branch exit design, and a matrix approximation technique. In addition, a multi-objective heuristic algorithm is employed to effectively balance the competing objectives in SAE optimization. Our results demonstrate that the proposed MO-SAE delivers substantial improvements over the original approach. On the x86 architecture, it reduces storage space and power consumption by at least 50%, improves runtime efficiency by no less than 28%, and achieves an 11.8% compression rate, all while maintaining application performance. Furthermore, MO-SAE runs efficiently on edge devices with ARM architecture. Experimental results show a 15% improvement in inference speed, facilitating efficient deployment in cloud-edge collaborative anomaly detection systems.