Continuous physiological signal monitoring and diagnosis are crucial for proactive health management and timely interventions. Key challenges include achieving non-toxic adhesion of stretchable conductors to dynamic skin and integration with lightweight, wearable circuits equipped diagnosing algorithms. We propose wireless physiological monitoring with vital diagnosis, featuring octopus-inspired micromembrane structure electrodes that enhance both adhesion and permeability. These stretchable electrodes exhibit a conductivity of over 2700 S/cm and maintain stretchability up to 1000 %, with minimal degradation after 1000 cycles of deformation. Adhesion reaches 12 kPa, ensuring durability for over 1000 attachment-detachment cycles and long-term attachment exceeding 24 h without skin toxicity. The system, connected to a miniaturized wireless circuit (2.8 g), facilitates real-time, accurate collection of electrocardiography (ECG), electromyography (EMG), electrooculography (EOG), and electroencephalography (EEG) signals. As proof of concept, ECG signals from real subjects processed with a transfer-learning algorithm achieved over 93.3 % diagnostic accuracy, paving the way for reliable, personalized health monitoring. • Achieved record-high conductivity (2700 S/cm) and 1000 % stretchability in a long-term stable stretchable conductor. • Skin-adhesive conductor maintained performance under 1000 cycles of strain, stretch, adhesion, and bio-signal reliability. • Wireless ECG monitoring showed over 93.3 % prediction accuracy using data from 15 individuals with normal heart rhythms.