Electrospun polymeric fibers can be used as strain sensors due to their large surface to weight/volume ratio, high porosity and pore interconnectivity. Large strain flexible strain sensors are used in numerous applications including rehabilitation, health monitoring, and sports performance monitoring where large strain detection should be accommodated by the sensor. This has boosted the demand for a stretchable, flexible and highly sensitive sensor able to detect a wide range of mechanically induced deformations. Herein, a physically cross-linked polylactic acid (PLA) and thermoplastic polyurethane (TPU) blend is made into nanofiber networks via electrospinning. The PLA/TPU weight ratio is optimized to obtain a maximum attainable strain of 100% while maintaining its mechanical integrity. The TPU/PLA fibers also allowed for their thermally activated recovery due to shape memory properties of the substrate. This novel feature enhances the sensor's performance as it is no longer limited by its plastic deformation. Using spray coating method, a homogeneous layer of single-walled carbon nanotube is deposited onto the as-spun fiber mat to induce electrical conductivity to the surface of the fibers. It is shown that stretching and bending the sensor result in a highly sensitive and linear response with a maximum gauge factor of 33.