Senior citizens face many challenges to their independent living. Fall and Parkinson's disease (PD) are among the most life-threatening events or conditions. Precise and prompt motion sensor-based assessments for fall risk and PD severity can lead to timely interventions that can relieve or ultimately eliminate the threats. However, past studies focus on ad hoc feature engineering, which is subjective and less transferrable to related domains. In this work, we propose a Deep Multi-source Multi-task Learning (DMML) approach that provides an integrated framework for sensor-based condition risk and severity assessment. We develop Convolutional Neural Networks (CNN) to extract features from sensor signals. We collect timed up and go (TUG) test data at a neurology clinic to evaluate our model. Five sensors are attached to 22 PD patients to collect motion data throughout the test. Our model achieves F-measure of 0.940 for assessing fall risks, and RMSE of 0.060 for assessing PD severities, significantly outperforming the benchmark methods.