We report a theoretical investigation on the effects of interface reconstruction on magnetic anisotropy (MA) and Dzyaloshinskii-Moriya interaction (DMI) for nonisostructural heterostructures formed by an infinite-layer oxide ${\mathrm{SrCuO}}_{2}$ and a perovskite oxide ${\mathrm{SrRuO}}_{3}$. Due to the atomic, charge, spin, and orbital reconstructions at interface, the SRO film thickness-dependent magnetic anisotropy oscillation behavior has been greatly tuned in two ${\mathrm{SrCuO}}_{2}/{\mathrm{SrRuO}}_{3}$ heterostructures. A strong DMI of 3.5 meV/Ru and a large DMI/exchange constant ratio $|D/J|$ of 0.63 are obtained at the ${\mathrm{CuO}}_{2}\text{\ensuremath{-}}\mathrm{Sr}\text{\ensuremath{-}}{\mathrm{RuO}}_{2}$ interface, which are beneficial to the creation and stability of skyrmions. Besides, the DMI is tunable, monotonically decreasing with the increase of the content of the apical oxygen ions in the interfacial layer, and takes the minimal value of 0.1 meV/Ru at the ${\mathrm{CuO}}_{2}\text{\ensuremath{-}}\mathrm{SrO}\text{\ensuremath{-}}{\mathrm{RuO}}_{2}$ interface. We evaluate the formation energy of oxygen vacancy in interface SRO layer, which turns out to be half as much as that in bulk SRO. This small value ensures the experimental feasibility towards two interfaces. Combining first-principles calculations with tight-binding model, we find that the effectively modulated MA and DMI at the ${\mathrm{CuO}}_{2}\text{\ensuremath{-}}\mathrm{Sr}\text{\ensuremath{-}}{\mathrm{RuO}}_{2}$ interface are mainly associated with the occupation of ${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ orbital, the enhanced interface symmetry breaking, and orbital hybridization. The present work demonstrates the distinct features of the interface formed between nonisostructural oxides and suggests a conceptually different strategy towards the modulation of MA and DMI.