For oxygen reduction reaction (ORR) over alloy electrocatalysts, the understanding of how the atomic arrangement of the metal species in the nanocatalysts is responsible for the catalytic enhancement is challenging for achieving better design and tailoring of nanoalloy catalysts. This paper reports results of an investigation of the atomic structures and the electrocatalytic activities of ternary and binary nanoalloys, aiming at revealing a fundamental insight into the unique atomic-scale structure-electrocatalytic activity relationship. PtIrCo catalyst and its binary counterparts (PtCo and PtIr) are chosen as a model system for this study. The effect of thermochemical treatment temperature on the atomic-scale structure of the catalysts was examined as a useful probe to the structure-activity correlation. The structural characterization of the binary and ternary nanoalloy catalysts was performed by combining surface sensitive techniques such as XPS and 3D atomic ordering sensitive techniques such as high-energy X-ray diffraction (HE-XRD) coupled to atomic pair distribution function (PDF) analysis (HE-XRD/PDFs) and computer simulations. The results show that the thermal treatment temperature tunes the nanoalloy's atomic and chemical ordering in a different way depending on the chemical composition, leading to differences in the nanoalloy's mass and specific activities. A unique structural tunability of the atomic ordering in a platinum-iridium-cobalt nanoalloy has been revealed for enhancing greatly the electrocatalytic activity toward oxygen reduction reaction, which has significant implication for rational design and nanoengineering of advanced catalysts for electrochemical energy conversion and storage.