We have studied the diffusion mechanism of lithium ions in glassy oxide-based solid state electrolytes using elastic and quasielastic neutron scattering. Samples of xLi2SO4-(1-x)(Li2O-P2O5) were prepared using conventional melt techniques. Elastic and inelastic scattering measurements were performed using the triple-axis spectrometer (TRIAX) at Missouri University Research Reactor at University of Missouri and High Flux Backscattering Spectrometer (HFBS) at NIST Center for Neutron Research, respectively. These compounds have a base glass compound of P2O5 which is modified with Li2O. Addition of Li2SO4 leads to the modification of the structure and to an increase lithium ion (Li+) conduction. We find that an increase of Li2SO4 in the compounds leads to an increase in the Lorentzian width of the fit for the quasielastic data, which corresponds to an increase in Li+ diffusion until an over-saturation point is reached (< 60% Li2SO4). We find that the hopping mechanism is best described by the vacancy mediated Chudley-Elliot model. A fundamental understanding of the diffusion process for these glassy compounds can help lead to the development of a highly efficient solid electrolyte and improve the viability of clean energy technologies.