Dislocations in van der Waals (vdW) layered nanomaterials induce strain and structural changes that substantially impact thermal transport. Understanding these effects could enable the manipulation of dislocations for improved thermoelectric and optoelectronic applications, but experimental insights remain limited. In this study, we use synthetic Eshelby twisted vdW GeS nanowires (NWs) with single screw dislocations as a model system to explore the interplay between dislocation-induced structural modifications and lattice thermal conductivity. Our measurements reveal a monoclinic structure stabilized by the dislocation, leading to a substantial drop in thermal conductivity for larger-diameter NWs (70% at room temperature), supported by first-principles calculations. Interestingly, we also find an anomalous enhancement of thermal conductivity with decreasing diameter in twisted NWs, contrary to typical trends in non-twisted GeS NWs. This is attributed to increased conductivity near the NW cores due to compressive strain around the central dislocations, and aligns with a density-functional-theory-informed core-shell model. Our results highlight the critical role of dislocations in thermal conduction, providing fundamental insights for defect and strain engineering in advanced thermal applications.