One of the most challenging forms of misinformation involves the out-of-context (OOC) use of images paired with misleading text, creating false narratives. Existing AI-driven detection systems lack explainability and require expensive fine-tuning. We address these issues with MAD-Sherlock: a Multi-Agent Debate system for OOC Misinformation Detection. MAD-Sherlock introduces a novel multi-agent debate framework where multimodal agents collaborate to assess contextual consistency and request external information to enhance cross-context reasoning and decision-making. Our framework enables explainable detection with state-of-the-art accuracy even without domain-specific fine-tuning. Extensive ablation studies confirm that external retrieval significantly improves detection accuracy, and user studies demonstrate that MAD-Sherlock boosts performance for both experts and non-experts. These results position MAD-Sherlock as a powerful tool for autonomous and citizen intelligence applications.