We report the microscopic origin of strain-mediated changes in the magnetocrystalline anisotropy energy of the Co2FeSi, Co2MnSi, and Fe3Si Heusler alloys from the viewpoint of first-principles electron theory. Both Co2FeSi and Co2MnSi have similar anisotropy changes upon induced strain within the (001) plane, where the quadrupole moment due to Co minority-spin states dominates the anisotropy modulation, and, thus, giant magnetoelectric couplings in multiferroic heterointerfaces containing these compounds. In contrast, the strain-induced anisotropy modulation in Fe3Si has mixed contributing factors not limited to the anisotropy term of the orbital magnetic moment and the quadrupole term.