Global aging necessitates tele-monitoring systems to provide real-time tracking and timely assistance for older adults living independently. While pervasive wireless devices (e.g., CSI, IMU, UWB) enable cost-effective, non-intrusive monitoring, existing systems lack flexibility, limiting their adaptability to different environments. In this work, we posit that the motion dynamics of human movement are invariant across sensing modalities, inspiring the design of HARMONY—a privacy-preserving, sensor-agnostic system that supports multi-modal inputs and diverse tele-monitoring tasks. HARMONY incorporates Modality-agnostic Data Processing to uniformly encrypt multi-modal signals and Task-specific Activity Recognition for seamless tasks adaptation. A novel Encrypted-processing Engine then significantly accelerates computations on encrypted data by optimizing matrix and convolution operations. Evaluations across five different sensing modalities show that HARMONY consistently achieves high accuracy while delivering 3.5 × to 130 × speedups over state-of-the-art baselines. Our results demonstrate that HARMONY is a practical, scalable, and privacy-centric prototype for next-generation remote healthcare.