A broad range of cationic nonstoichiometry has been demonstrated for the Li-rich layered rock-salt-type oxide Li2MoO3, which has generally been considered as a phase with a well-defined chemical composition. Li2+xMo1-xO3 (-0.037 ≤ x ≤ 0.124) solid solutions were synthesized via hydrogen reduction of Li2MoO4 in the temperature range of 650-1100 °C, with x decreasing with the increase of the reduction temperature. The solid solutions adopt a monoclinically distorted O3-type layered average structure and demonstrate a robust local ordering of the Li cations and Mo3 triangular clusters within the mixed Li/Mo cationic layers. The local structure was scrutinized in detail by electron diffraction and aberration-corrected scanning transmission electron microcopy (STEM), resulting in an ordering model comprising a uniform distribution of the Mo3 clusters compatible with local electroneutrality and chemical composition. The geometry of the triangular clusters with their oxygen environment (Mo3O13 groups) has been directly visualized using differential phase contrast STEM imaging. The established local structure was used as input for density functional theory (DFT)-based calculations; they support the proposed atomic arrangement and provide a plausible explanation for the staircase galvanostatic charge profiles upon electrochemical Li+ extraction from Li2+xMo1-xO3 in Li cells. According to DFT, all electrochemical capacity in Li2+xMo1-xO3 solely originates from the cationic Mo redox process, which proceeds via oxidation of the Mo3 triangular clusters into bent Mo3 chains where the electronic capacity of the clusters depends on the initial chemical composition and Mo oxidation state defining the width of the first charge low-voltage plateau. Further oxidation at the high-voltage plateau proceeds through decomposition of the Mo3 chains into Mo2 dimers and further into individual Mo6+ cations.