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We present a 23Na nuclear spin dynamics model for interpreting nuclear magnetic resonance (NMR) spin-lattice relaxation and central linewidth data in the invert glass system Na4P2S7-xOx, 0 ≤ x ≤ 7. The glassy nature of this material results in variations in local Na+ cation environments that may be described by a Gaussian distribution of activation energies. A consistent difference between the mean activation energies determined by NMR and DC conductivity measurements was observed, and interpreted using a percolation theory model. From this, the Nasingle bondNa coordination number in the sodium cation sublattice was obtained. These values were consistent with jumps through tetrahedral faces of the sodium cages for the sulfur rich glasses, x < 5, consistent with proposed models of their short range order (SRO) structures. From NMR spin-echo measurements, we determined the Nasingle bondNa second moment M2 resulting from the Nasingle bondNa magnetic dipole interaction of nearest neighbors. Values of M2 obtained as a function of sodium number density N were in agreement with models for uniform sodium distribution, indicating that these invert glass systems form so as to maximize the average Nasingle bondNa distance. A simple Coulombic attraction model between Na+ cation and X (=S−, O−) anion was applied to calculate the activation energy. In the range 1.5 ≤ x ≤ 7, an increase in activation energy with increasing oxygen content x occurred, and was consistent with the decrease in average anionic radius, and the increase in Coulombic attraction. For small oxygen additions, 0 ≤ x ≤ 1.5, the suggested minimum at low oxygen concentration seen in the activation energies obtained from DC conductivity data is not evident in the model.