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The effects of uniaxial compressive stress on the normal state ^{17}O nuclear-magnetic-resonance properties of the unconventional superconductor Sr_{2}RuO_{4} are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal a-axis strain ϵ_{aa}≡ϵ_{v} that maximizes the superconducting transition temperature T_{c}. The spin susceptibility weakly increases on lowering the temperature below T≃10  K, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the γ band formed by the Ru d_{xy} states hybridized with in-plane O p_{π} orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalization S by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.