Crystalline oxide semiconductors are promising back-end-of-line (BEOL)-compatible channel materials for AI hardware, yet their nanoscale trap physics remains unclear. Here, we directly mapped and quantified mobility (μ), trap density (<i>N</i>_eff), and trap depth in amorphous/nanocrystalline (a/n-) and polycrystalline (p-) In₂O₃ films using scanning noise microscopy with finite-element analysis. A/n-In₂O₃ exhibited large local variations in μ and <i>N</i>_eff with deep trap states (∼0.24 eV). Upon full crystallization, p-In₂O₃ exhibited uniform μ and <i>N</i>_eff with shallow trap states at grains (∼0.10 eV) and grain boundaries (∼0.12 eV). Crystallization effectively eliminated structural-disorder-induced deep states, leaving only shallow donor-like oxygen vacancy traps. This led to enhanced μ and significantly reduced <i>N</i>_eff (and trap depth), exhibiting uniform spatial distributions with minute changes at grain boundaries. Furthermore, p-In₂O₃ devices achieved higher mobility, more positive threshold voltage, and improved bias stability, confirming reduced deep-trap activity and enhanced charge-transport uniformity. This work establishes a direct link between structural ordering, local trap-depth modulation, and macroscopic electrical performances of crystalline oxide channels.