We present GenECA, a general-purpose framework for real-time multimodal interaction with embodied conversational agents. GenECA captures audio and visual signals from standard devices to analyze nonverbal features such as facial expressions, vocal tone, gaze, and posture. This information is used to generate context-aware dialogue and synchronize the agent's speech with dynamic gestures and backchannel facial animations in real time. GenECA provides the first ECA system able to deliver context-aware speech and well-timed animations in real-time without reliance on human operators. Through modular design, it can support a wide variety of applications, such as education, customer service, and therapy. Our research enables rapid prototyping and deployment of interactive virtual agents.