Sub-nanometer metal oxide clusters are very important materials that are widely used, for example, in catalysis or electronic devices such as sensors. Hence, it is critical to understand the atomic structures and properties of sub-nanometer metal oxide clusters under a reactive gas environment, such as O2. We consider here experimentally accessible precise-size Cu clusters (Cu4) supported on partially hydroxylated amorphous alumina and show that such clusters can access, in catalytic conditions at high temperature under a pressure of O2, a large ensemble of oxidized structures, representing a large variety of oxygen content, of geometries in link with the support, and of catalytic activities for oxidation reactions, as seen from their reducibilities. A grand canonical basin hopping method based on first-principles energy reveals an ensemble of 24 configurations for the Cu4Ox cluster of low free energy, less than 0.8 eV above the global minimum. The low free energy ensemble consists of clusters of different stoichiometries, which are mainly Cu4O3 and Cu4O4 in the temperature range of 200–400 °C and under a pressure of 0.5 bar of O2. The presence of several competitive isomers at each composition implies that cluster fluxionality impacts the phase diagram, which should be ensemble-averaged. In terms of catalytic oxidation activity, Cu4O3 isomers present highly variable O abstraction energy: the most stable isomers are inactive for alkane oxidative dehydrogenation, but isomerization to metastable isomers, that proceed with low barrier, enable to create active configurations with low O abstraction energy. O atoms with the lowest anionic character, and thus of more electrophilic nature, present the best oxidation capability. In contrast, all Cu4O4 isomers show a low O abstraction energy and a high potential catalytic activity. This manuscript demonstrates the unique structural and electronic properties of sub-nano Cu oxide clusters and illustrates the critical roles of configuration ensembles and rearrangement to highly reactive metastable cluster isomers in nanocatalysis.