Highly sensitive pressure sensors with biocompatibility, biodegradability, and flexibility are needed in robotics, prostheses, medical implants, and wearable electronics. However, it is challenging to fabricate a pressure sensor with all these attributes due to material limitations or technological bottlenecks. Herein, we present a silk- Polyvinyl Alcohol (S-PVA) composite nanofiber-based flexible, biocompatible, and biodegradable capacitive pressure sensor developed using a facile and cost-effective screen-printing approach. The screen-printed silver was used as the top and bottom electrodes, with flexible and biodegradable chitosan as a substrate. The device exhibited extremely wide pressure sensing range varying from ~1 kPa to 800 kPa with a maximum sensitivity of ~2.83 kPa-1 (<10kPa) and fast response and recovery time of ~35 and ~40 ms. The high sensitivity in the low-pressure region is primarily due to the high porosity and surface area, and reduction in the effective distance between the multilayers of 1D S-PVA nanofibers. The device shows excellent cyclic repeatability and good stepwise cyclic increment in both low- and high-pressure regions for more than 2×103 and 3.2×103 cycles, respectively. Next, a flexible memristor is fabricated and integrated with the fabricated pressure sensor to emulate the functionality of the artificial sensory nervous system, with the memristor acting as a synapse and the pressure sensor acting as a mechanoreceptor. Different materials like Zinc Oxide, silicon nitride etc. have been explored as the active layer of the memristor device and the devices exhibit excellent repeatability and data retention property.  Finally, the biodegradability tests reveal that the device completely dissolved in pure DI water at room temperature in less than 24 hours. Thus, the novel S-PVA composite based nanofiber serves as an excellent biomaterial and paves the path for next generation wearable and implantable medical device applications.