Fiber-based sensor based on the core-sheath structure has drawn increasing attention in the strain sensing and self-powered fields because of its various advantages (e.g., lightweight, small size, flexibility and ease of weavability into soft textile, etc.). However, it still has been challenging to continuously fabricate core-sheath fiber with good interfacial interaction. Herein, a core-sheath fiber was continuously fabricated by melt co-extrusion molding method, whose sheath layer and core layer are respectively pure polystyrene polybutadiene polystyrene (SBS) and SBS/multi-walled carbon nanotubes (SBS/MWCNTs) composite. In view of this, exhibits good compatibility occurs between core layer and sheath layer because they share the same SBS phase. Moreover, with the help of sheath layer, core layer can be effectively prevented the environmental damage. Fiber strain sensor based on such core-sheath fiber exhibits a higher sensitivity (i.e., GF = 106341), wider working range (strain of 0–200 %) and shorter response time (50 ms), which can further perform underwater communication and underwater motion monitoring. Furthermore, based on such core-sheath fiber, fiber triboelectric generator (F-TENG) and textile triboelectric generator (T-TENG) have been successfully developed and they can respectively serve as self-powered bionic whisker (SPBW) and mechanical energy harvester (MEH). This study provides a facile, low-cost, continuous and environmentally friendly method to fabricate core-sheath fiber, paving a new pathway to develop fiber with strain sensing and self-powered sensing performance.