We report the discovery of extraordinarily large anisotropy fields and strain-tunable magnetocrystalline anisotropy in ${\mathrm{Sr}}_{2}{\mathrm{CrReO}}_{6}$ epitaxial films. We determine the strain-induced tetragonal distortions and octahedral rotations in ${\mathrm{Sr}}_{2}{\mathrm{CrReO}}_{6}$ epitaxial films grown on (${\mathrm{LaAlO}}_{3}$)${}_{0.3}$(${\mathrm{Sr}}_{2}{\mathrm{AlTaO}}_{6}$)${}_{0.7}$ (LSAT), ${\mathrm{SrTiO}}_{3}$ (STO), and ${\mathrm{SrCr}}_{0.5}{\mathrm{Nb}}_{0.5}{\mathrm{O}}_{3}$/LSAT substrates using x-ray diffraction and density functional theory. The structural distortions drive dramatic changes in magnetocrystalline anisotropy. We use magnetometry measurements and first principles calculations to determine the atomic origins of the large anisotropy observed. These techniques elucidate the interplay between structural deformations and magnetic behavior and lay the groundwork for the study of other strongly correlated systems in this class of ferromagnetic oxides.