We explicitly analyze $O\left({\alpha }^{\prime }\right)$ corrections to heterotic supergravity on toroidal orbifolds and their resolutions, which play important roles in string phenomenology as well as moduli stabilization. Using a conformal factor ansatz that is valid only for four-dimensional geometries, we obtain a closed expression for the $O\left({\alpha }^{\prime }\right)$ metric corrections in the case of several orbifold limits of K3, namely $T^4/Z_n$ where $n=2$, 3, 4, 6. However, we find that nonstandard embedding requires the inclusion of five-branes on such orbifolds. We also numerically investigate the behavior around orbifold fixed points by considering the metric correction on the resolution of a $C^2/Z_2$ singularity. In this case, a nontrivial conformal factor can be obtained in nonstandard embedding even without five-branes. In the same manner, we generalize our analysis to study metric corrections on $T^6/Z_3$ and its resolution described by a complex line bundle over ${\mathrm{CP}}^2$. Further prospects of utilizing these $O\left({\alpha }^{\prime }\right)$ corrected metrics as a novel approach in obtaining realistic or semirealistic Yukawa couplings are discussed.