Capabilities in continuous monitoring of key physiological parameters of disease have never been more important than in the context of the global COVID-19 pandemic. Soft, skin-mounted electronics that incorporate high-bandwidth, miniaturized motion sensors represent a powerful class of technology for digital, wireless measurements of mechano-acoustic (MA) signatures of both core vital signs (heart rate, respiratory rate, and temperature) and underexplored biomarkers (coughing count) with high fidelity and immunity to ambient noises. Here, we introduce an effort that integrates such an MA sensor, a cloud data infrastructure and data analytics approaches based on digital filtering and convolutional neural networks for comprehensive monitoring of COVID-19 infections in sick and healthy individuals in a population, both in the hospital and the home. This hardware/software system extracts diverse signatures of health status in an automated fashion from a single device and time series data stream. Unique features are in quantitative measurements of coughing and other vocal events, as indicators of both disease and infectiousness. Systematic imaging studies demonstrate direct correlations between the time and intensity of coughing, speaking and laughing and the total droplet production, as an approximate indicator of the probability for disease spread. The sensors, deployed on COVID-19 patients along with healthy controls in both inpatient and home settings, record coughing frequency and intensity continuously, along with a comprehensive collection of other biometrics, with recording times for individuals of more than a month after disease diagnosis. These pilot studies include 3,111 hours of data spanning 363 days from 37 COVID-19 patients (20 females, 17 males) with 27,651 coughs detected in total along with continuous measurements of heart rate, respiratory rate, physical activity, and skin temperature. Manual labeling of randomly sampled 10,258 vocal events from 11 COVID-19 patients (6 females, 5 males) suggests a sensitivity of 85% and a specificity of 96% in cough detection using automated algorithms. The collective results indicate a decaying trend of coughing frequency and intensity through the course of disease recovery, but with wide variations across patient populations. The methodology also opens opportunities to study patterns in biometrics across individuals and among different demographic groups.