Stretchable and conductive nanocomposites are emerging as important constituents of soft mechanical sensors for health monitoring, human-machine interactions, and soft robotics. However, tuning the materials' properties and sensor structures to the targeted mode and range of mechanical stimulation is limited by current fabrication approaches, particularly in scalable polymer melt techniques. Here, thermoplastic elastomer-based nanocomposites are engineered and novel rheological requirements are proposed for their compatibility with fiber processing technologies, yielding meters-long, soft, and highly versatile stretchable fiber devices. Based on microstructural changes in the nanofiller arrangement, the resistivity of the nanocomposite is tailored in its final device architecture across an entire order of magnitude as well as its sensitivity to strain via tuning thermal drawing processing parameters alone. Moreover, the prescribed electrical properties are coupled with suitable device designs and several fiber-based sensors are proposed aimed at specific types of deformations: i) a robotic fiber with an integrated bending mechanism where changes as small as 5 degrees are monitored by piezoresistive nanocomposite elements, ii) a pressure-sensing fiber based on a geometrically controlled resistive signal that responds with a sub-newton resolution to changes in pressing forces, and iii) a strain-sensing fiber that tracks changes in capacitance up to 100% elongation.