Large Language Models (LLMs) excel at a range of tasks but often struggle with issues like hallucination and inadequate empathy support. To address hallucinations, we ground our dialogues in medical knowledge sourced from external repositories such as Disease Ontology and DrugBank. To improve empathy support, we develop the Empathetic Healthcare Dialogues dataset, which utilizes multiple dialogue strategies in each response. This dataset is then used to fine-tune an LLM, and we introduce a lightweight, adaptable method called Strategy Combination Guidance to enhance the emotional support capabilities of the fine-tuned model, named EHDChat. Our evaluations show that EHDChat significantly outperforms existing models in providing emotional support and medical accuracy, demonstrating the effectiveness of our approach in enhancing empathetic and informed AI interactions in healthcare.