Stretchable strain sensors are crucial in various applications, such as human health monitoring and soft robotics. Understanding the intricate relationship between material properties and sensor performance is essential for the technology's future progress. In this study, we developed three types of flexible strain sensors by embedding conductive nanofibrous mats in polydimethylsiloxane (PDMS). The nanofibrous mats were composed of silica-poly(3,4-ethylenedioxythiophene) (silica-PEDOT), poly(vinylidene fluoride)-PEDOT (PVDF-PEDOT), and carbon nanofibers (CNFs), each with a different Young's modulus, achieved through electrospinning, carbonization, and vapor phase polymerization techniques. The results of tensile testing and sensor characterization were analyzed using an electron tunneling model, which revealed that changes in resistance were influenced by alterations in conductive pathways. Notably, our investigation established a direct correlation between the Young's modulus and the sensitivity/stretchability of each strain sensor. A protype "smart"glove using stretchable sensors was demonstrated to remotely control the motion of a robotic hand.