A versatile medical image segmentation model applicable to imaging data collected with diverse equipment and protocols can facilitate model deployment and maintenance. However, building such a model typically requires a large, diverse, and fully annotated dataset, which is rarely available due to the labor-intensive and costly data curation. In this study, we develop a cost-efficient method by harnessing readily available data with partially or even sparsely annotated segmentation labels. We devise strategies for model self-disambiguation, prior knowledge incorporation, and imbalance mitigation to address challenges associated with inconsistently labeled data from various sources, including label ambiguity and imbalances across modalities, datasets, and segmentation labels. Experimental results on a multi-modal dataset compiled from eight different sources for abdominal organ segmentation have demonstrated our method's effectiveness and superior performance over alternative state-of-the-art methods, highlighting its potential for optimizing the use of existing annotated data and reducing the annotation efforts for new data to further enhance model capability.