We present the approaches and contributions of the winning team NimbRo@Home at the RoboCup@Home 2024 competition in the Open Platform League held in Eindhoven, NL. Further, we describe our hardware setup and give an overview of the results for the task stages and the final demonstration. For this year's competition, we put a special emphasis on open-vocabulary object segmentation and grasping approaches that overcome the labeling overhead of supervised vision approaches, commonly used in RoboCup@Home. We successfully demonstrated that we can segment and grasp non-labeled objects by text descriptions. Further, we extensively employed LLMs for natural language understanding and task planning. Throughout the competition, our approaches showed robustness and generalization capabilities. A video of our performance can be found online.