Stress analysis plays a critical role in the engineering design process, enabling the characterization of mechanical behavior and prediction of material failure in structural alloys for structural application. However, in polycrystalline engineering alloys, the intrinsic anisotropic properties of the constituent single-crystal structures lead to the development of heterogeneous, multi-axial stress fields while under mechanical load. Traditional continuum-based mechanical characterization and modeling approaches often lack the fidelity to resolve these complex spatial variations of stress that ultimately govern material failure mechanisms in engineering alloys. Additionally, accurate determination of single-crystal constituents\textemdash single-crystal elastic moduli\textemdash remains a significant challenge for most real-world alloys due to the impracticality of direct bulk single-crystal fabrication and mechanical testing. To address these limitations, this work integrates High-Energy X-ray Diffraction Microscopy (HEDM) with polycrystalline modeling to develop and validate experimental-computational frameworks for micro-mechanical characterization. First, a methodology is introduced for extracting single-crystal elastic moduli directly from polycrystalline materials. This approach combines grain-averaged elastic lattice strain measurements from \textit{in situ} HEDM mechanical loading experiments with an inverse optimization framework to determine the set of elastic constants that best reproduce the observed macroscopic material response. Second, this work investigates the sensitivity of the extracted single-crystal elastic moduli to the level of microstructural detail used to instantiate the virtual polycrystalline mechanical model used in the optimization. Parametric studies are conducted in which both the topology and polycrystal population network of the microstructure are systematically and randomly altered, estimating baseline thresholds necessary for determining single-crystal elastic moduli. Finally, a framework is validated for reconstructing sub-granular stress fields from grain-averaged experimental HEDM measurements. This approach leverages reduced-order spherical harmonic series expansions over the sub-granular domain and equilibrium constraints derived from fundamental solid mechanics to construct a mechanistically constrained inverse optimization framework. The collective body of work in this thesis aims to further the fundamental understanding of stress in anisotropic polycrystalline materials and its distribution across material length scales for mechanical design.