Layered sodium transition-metal (TM) oxides, NaₓTMO₂, are among the most promising sodium-ion positive electrode materials, yet their Na/vacancy orderings, layer stacking sequences, and cooperative Jahn–Teller distortions are known only for a few single-TM compounds. We compile the Na/vacancy orderings reported in earlier studies into a single library of 41 unique orderings and apply this uniformly to five single-TM and all ten NaₓTM_(0.5)TM'_(0.5)O₂ oxides (TM = Ti, Mn, Fe, Co, Ni), screening more than 120,000 structures with machine-learning interatomic potentials prior to 1,025 accurate first-principles calculations. The phase diagrams explain the observed O3/P3/O1 sequences and voltages, and the O3-to-P3 competition hinges on ordering energies of a few meV per atom that scalar descriptors, such as the cationic potential and the interlayer-slab distance, miss. Our extensive analysis reveals that the redox couples form a nearly partner-independent ladder, Ti^(3+/4+) < Mn^(3+/4+) < Co^(3+/4+) < Ni^(2+/3+) < Fe^(3+/4+), explaining pristine charge transfer and the oxidation sequence. Van Vleck analysis of every TMO₆ octahedron reveals that TM mixing suppresses the cooperative Jahn–Teller distortions of Mn³⁺ and Ni³⁺ through charge transfer to Jahn–Teller-inactive states or dilution of Jahn–Teller-active centers. We formulate an energy-density-versus-strain map that yields a design rule: a high-voltage couple without Jahn–Teller strain, which Mn⁴⁺/Ni²⁺ charge transfer realizes in NaₓMn_(0.5)Ni_(0.5)O₂, the most practical composition. We release the ordering-resolved dataset as a training set for subsequent training of accurate machine-learning interatomic potentials.