Electrospun nanomesh electrodes offer excellent mechanical conformity and breathability for skin-integrated electronics. However, conventional randomly oriented structures exhibit isotropic behavior, limiting functional adaptability. Here, a geometry-driven approach is presented to achieve electromechanical anisotropy by aligning fibers within free-standing, monolayer nanomesh electrodes. Through parylene vapor coating and gold evaporation, devices are fabricated that respond distinctly when strained parallel or perpendicular to the fiber alignment. Under parallel strain, the mesh undergoes direct fiber elongation and gold fracture, resulting in a high gauge factor ideal for strain sensing. Conversely, perpendicular strain induces pore elongation and maintains inter-fiber connections, stabilizing resistance change and enabling use as a stretchable interconnect. These anisotropic behaviors are maintained under extreme conditions, with no elastomeric support and full metallic coverage. Quantitative analysis of pore aspect ratio dynamics reveals that deformation mode-fiber or pore-driven-is governed by strain direction, explaining the trade-off between sensitivity and mechanical durability. The breathable, elastomer-free design ensures skin compatibility for long-term use, while parylene passivation effectively shields the electrode from ionic interference caused by sweat and biofluids. This work introduces a tunable, dual-functional nanomesh platform optimized for electronic-skin applications, offering a unified solution for both sensing and interconnection demands in wearable electronics.