The convergence of the Internet of Things (IoT) with edge computing has created the Edge of Things (EoT), enabling real-time analytics but also expanding the cyber-attack surface. Traditional centralized Intrusion Detection Systems (IDS) are ill-suited for such decentralized, latency-sensitive environments. This paper presents FLEX-IDS, a federated, explainable, and adversarially robust IDS framework for heterogeneous EoT networks. FLEX-IDS combines five federated optimizers (FedAvg, FedOpt, FedProx, FedNova, FedPer) with cryptographic safeguards and post-hoc interpretability (SHAP and LIME) to ensure privacy, resilience, and transparency. Evaluated on three benchmark datasets CICIDS2017, UNSW-NB15, and ToN-IoT, the system achieves up to 98.05% accuracy and maintains a mean F1-score of 0.86 under 30% malicious participation. FLEX-IDS demonstrates energy efficiency (0.03–0.16 J/round) and edge-feasible explainability, achieving SHAP fidelity of 0.97. These results highlight FLEX-IDS as a scalable, secure, and interpretable intrusion detection solution for next-generation IoT infrastructures.