Intelligent edge machine learning has emerged as a paradigm for deploying smart applications across resource-constrained devices in next-generation network infrastructures. This survey addresses the critical challenges of implementing machine learning models on edge devices within distributed network environments, including computational limitations, memory constraints, and energy-efficiency requirements for real-time intelligent inference. We provide comprehensive analysis of soft computing optimization strategies essential for intelligent edge deployment, systematically examining model compression techniques including pruning, quantization methods, knowledge distillation, and low-rank decomposition approaches. The survey explores intelligent MLOps frameworks tailored for network edge environments, addressing continuous model adaptation, monitoring under data drift, and federated learning for distributed intelligence while preserving privacy in next-generation networks. Our work covers practical applications across intelligent smart agriculture, energy management, healthcare, and industrial monitoring within network infrastructures, highlighting domain-specific challenges and emerging solutions. We analyze specialized hardware architectures, cloud offloading strategies, and distributed learning approaches that enable intelligent edge computing in heterogeneous network environments. The survey identifies critical research gaps in multimodal model deployment, streaming learning under concept drift, and integration of soft computing techniques with intelligent edge orchestration frameworks for network applications. These gaps directly manifest as open challenges in balancing computational efficiency with model robustness due to limited multimodal optimization techniques, developing sustainable intelligent edge AI systems arising from inadequate streaming learning adaptation, and creating adaptive network applications for dynamic environments resulting from insufficient soft computing integration. This comprehensive roadmap synthesizes current intelligent edge machine learning solutions with emerging soft computing approaches, providing researchers and practitioners with insights for developing next-generation intelligent edge computing systems that leverage machine learning capabilities in distributed network infrastructures.