Misinformation continues to pose a significant challenge in today's information ecosystem, profoundly shaping public perception and behavior. Among its various manifestations, Out-of-Context (OOC) misinformation is particularly obscure, as it distorts meaning by pairing authentic images with misleading textual narratives. Existing methods for detecting OOC misinformation predominantly rely on coarse-grained similarity metrics between image-text pairs, which often fail to capture subtle inconsistencies or provide meaningful explainability. While multi-modal large language models (MLLMs) demonstrate remarkable capabilities in visual reasoning and explanation generation, they have not yet demonstrated the capacity to address complex, fine-grained, and cross-modal distinctions necessary for robust OOC detection. To overcome these limitations, we introduce EXCLAIM, a retrieval-based framework designed to leverage external knowledge through multi-granularity index of multi-modal events and entities. Our approach integrates multi-granularity contextual analysis with a multi-agent reasoning architecture to systematically evaluate the consistency and integrity of multi-modal news content. Comprehensive experiments validate the effectiveness and resilience of EXCLAIM, demonstrating its ability to detect OOC misinformation with 4.3% higher accuracy compared to state-of-the-art approaches, while offering explainable and actionable insights.