Multimodal Large Language Models have shown promising capabilities in bridging visual and textual reasoning, yet their reasoning capabilities in Open-Vocabulary Human-Object Interaction (OV-HOI) are limited by cross-modal hallucinations and limited viewpoints of images. To address this, we propose ImagineAgent, an agentic framework that integrates cognitive mapping, tool-augmented reinforcement learning (RL), and generative world modeling for robust OV-HOI understanding. Specifically, we first propose an innovative CoT dataset named hicodet-6K for supervised fine-tuning (SFT), which effectively bridges the perception-to-cognition gap by structuring perceived entities into interaction pairs for comprehensive predictions. Subsequently, we develop a multimodal tool library integrating online retrieval, image cropping, and generative modeling, enabling the agent to dynamically augment reasoning with domain-specific tools to resolve visual-semantic ambiguities and hallucinations during inference. Moreover, we incorporate a generative model to reconstruct alternative viewpoints, enabling the agent to 'imagine' under limited viewpoints. Finally, we propose a composite reward mechanism to jointly optimize prediction accuracy and tool efficiency. Evaluations on both SWIG-HOI and HICO-DET datasets demonstrate that our method achieves state-of-the-art performance while requiring merely 36.7% of the training data compared to existing methods, validating our robustness, empirical effectiveness and efficiency.