Retrieval-augmented generation (RAG) enhances large language models (LLMs) by incorporating external knowledge. Current hybrid RAG system retrieves evidence from both knowledge graphs (KGs) and text documents to support LLM reasoning. However, it faces challenges like handling multi-hop reasoning, multi-entity questions, multi-source verification, and effective graph utilization. To address these limitations, we present HydraRAG, a training-free framework that unifies graph topology, document semantics, and source reliability to support deep, faithful reasoning in LLMs. HydraRAG handles multi-hop and multi-entity problems through agent-driven exploration that combines structured and unstructured retrieval, increasing both diversity and precision of evidence. To tackle multi-source verification, HydraRAG uses a tri-factor cross-source verification (source trustworthiness assessment, cross-source corroboration, and entity-path alignment), to balance topic relevance with cross-modal agreement. By leveraging graph structure, HydraRAG fuses heterogeneous sources, guides efficient exploration, and prunes noise early. Comprehensive experiments on seven benchmark datasets show that HydraRAG achieves overall state-of-the-art results on all benchmarks with GPT-3.5-Turbo, outperforming the strong hybrid baseline ToG-2 by an average of 20.3% and up to 30.1%. Furthermore, HydraRAG enables smaller models (e.g., Llama-3.1-8B) to achieve reasoning performance comparable to that of GPT-4-Turbo. The source code is available on https://stevetantan.github.io/HydraRAG/.