Sluggish oxygen reduction reaction (ORR) remains a critical barrier to advancing intermediate-temperature electrochemical energy devices. Here, we demonstrate that strain engineering in two platforms, epitaxial thin films and freestanding membranes, systematically tunes ORR kinetics in Ruddlesden-Popper LaSrCoO4. In epitaxial films, the thickness is varied to control in-plane tensile strain, whereas in freestanding membranes strain relaxation during the release step of fabrication with water soluble sacrificial layers produces flat or wrinkled architectures. Electrochemical impedance spectroscopy analysis reveals more than an order of magnitude increase in the oxygen surface exchange coefficient for tensile-strained films relative to relaxed films, together with a larger oxygen vacancy concentration. Wrinkled freestanding membranes provide a further increase in oxygen surface exchange kinetics and a lower activation energy, which are attributed to increased active surface area and local strain variation. These results identify epitaxial tensile strain and controlled wrinkling as practical design parameters for optimizing ORR activity in Ruddlesden-Popper oxides.