Sleep staging and the assessment of sleep-disordered breathing (SDB) severity are critical tasks in clinical sleep medicine. However, existing deep learning models are typically trained on single-source centralized datasets, limiting their generalization and scalability across diverse populations and institutions. In this study, we propose a federated multi-task learning (FMTL) framework that enables collaborative model training across multiple datasets while preserving data privacy. Our approach simultaneously performs sleep staging and SDB severity classification using a shared feature extractor and task-specific branches, tailored to the heterogeneous distributions of different datasets. We simulate a realistic federated setting using five public PSG datasets—SHHS, APPLES, Sleep-EDF-X, HMC, and DREAMT—each treated as an independent client with non-identical data distributions. Experiments demonstrate that our FMTL framework outperforms conventional centralized and non-federated baselines in both sleep staging accuracy and SDB classification robustness, particularly under non-IID conditions. This work highlights the potential of federated learning to enable privacy-preserving, scalable, and generalizable sleep disorder modeling in real-world clinical applications.