Multinary lithium oxides with the rock salt structure are of technological importance as cathode materials in rechargeable lithium ion batteries. Current state-of-the-art cathodes such as LiNi1/3Mn1/3Co1/3O2 rely on redox cycling of earth-abundant transition-metal cations to provide charge capacity. Recently, the possibility of using the oxide anion as a redox center in Li-rich rock salt oxides has been established as a new paradigm in the design of cathode materials with enhanced capacities (>200 mAh/g). To increase the lithium content and access electrons from oxygen-derived states, these materials typically require transition metals in high oxidation states, which can be easily achieved using d(0) cations. However, Li-rich rock salt oxides with high valent d(0) cations such as Nb5+ and Mo6+ show strikingly high voltage hysteresis between charge and discharge, the origin of which is uninvestigated. In this work, we study a series of Li-rich compounds, Li4+xNi1-xWO6 (0 <= x <= 0.25) adopting two new and distinct cation-ordered variants of the rock salt structure. The Li4.15Ni0.85WO6 (x = 0.15) phase has a large reversible capacity of 200 mAh/g, without accessing the Ni3+/Ni4+ redox couple, implying that more than two-thirds of the capacity is due to anionic redox, with good cyclability. The presence of the 5d(0) W6+ cation affords extensive (>2 V) voltage hysteresis associated with the anionic redox. We present experimental evidence for the formation of strongly stabilized localized O-O single bonds that explain the energy penalty required to reduce the material upon discharge. The high valent d(0) cation associates localized anion-anion bonding with the anion redox capacity.