Large Language Models (LLMs) have demonstrated promising potential in providing empathetic support during interactions. However, their responses often become verbose or overly formulaic, failing to adequately address the diverse emotional support needs of real-world scenarios. To tackle this challenge, we propose an innovative strategy-enhanced role-playing framework, designed to simulate authentic emotional support conversations. Specifically, our approach unfolds in two steps: (1) Strategy-Enhanced Role-Playing Interactions, which involve three pivotal roles -- Seeker, Strategy Counselor, and Supporter -- engaging in diverse scenarios to emulate real-world interactions and promote a broader range of dialogues; and (2) Emotional Support Agent Training, achieved through fine-tuning LLMs using our specially constructed dataset. Within this framework, we develop the \textbf{ServeForEmo} dataset, comprising an extensive collection of 3.7K+ multi-turn dialogues and 62.8K+ utterances. We further present \textbf{SweetieChat}, an emotional support agent capable of handling diverse open-domain scenarios. Extensive experiments and human evaluations confirm the framework's effectiveness in enhancing emotional support, highlighting its unique ability to provide more nuanced and tailored assistance.