Strain engineering offers unique control to manipulate the electronic band structure of two-dimensional (2D) materials, resulting in an effective and continuous tuning of the physical properties. Ad hoc straining of 2D materials has demonstrated state of the art photonic devices including efficient photodetectors at telecommunication frequencies, enhanced-mobility transistors, and on-chip single photon sources, for example. However, in order to gain insights into the underlying mechanism required to enhance the performance of the next-generation devices with strain(op)tronics, it is imperative to understand the nano- and microscopic properties as a function of a strong nonhomogeneous strain. Here, we study the strain-induced variation of local conductivity of a few-layer transition metal dichalcogenide using conductive atomic force microscopy. We report a strain characterization technique by capturing the electrical conductivity variations induced by local strain originating from surface topography at the nanoscale, which allows overcoming limitations of existing optical spectroscopy techniques. We show that the conductivity variations parallel the strain deviations across the geometry predicted by molecular dynamics simulation. These results substantiate a variation of the effective mass and surface charge density by 0.026me and 0.03e for every percent of uniaxial strain, respectively, derived using band structure calculation based on the first-principles density functional theory. Furthermore, we demonstrate modulation of the effective Schottky barrier height by quantifying its alteration originating from a gradual reduction of the conduction band minima as a function of tensile strain. Such spatially textured electronic behavior via surface topography-induced strain variations in atomistic-layered materials at the nanoscale opens up exciting opportunities to control fundamental material properties and offers a myriad of design and functional device possibilities, such as for electronics, nanophotonics, flextronics, or smart cloths.