Adhesive hydrogels have gained great interest for biomedical applications, because of their great adhesion, tunable structure, high water content, and biocompatibility. However, it is still challenging to engineer hydrogel materials combining tissue repairs and strain sensors. In this work, poly(thioctic acid) (PTA) is used as a skeleton structure and mixed with polydopamine (PDA), resulting in hydrogels with excellent stretchability, resilience, and adhesion, which can adhere to various organic (porcine skin) and inorganic materials (ceramic, wood, glass, etc.) in both dry and wet environments. The hydrogels also exhibit antiswelling behavior, self-healing, and repeatable adhesion capacity (seven times), which are meaningful for bioapplications and show satisfactory biocompatibility, biodegradation, cell affinity, and ability to limit apoptosis in both in vitro and in vivo experiments. In the full-thickness skin defect model, the hydrogels can accelerate the wound healing process. The introduction of Fe3+ can significantly enhance the conductivity of the hydrogels, making it possible for the hydrogels to be used as strain sensors. This functional hydrogel may find an appealing application as an antiswelling and durability adhesive for strain sensors.