While solid-state NMR spectroscopic techniques have helped clarify the local structure and dynamics of ionic conductors, similar studies of mixed ionic-electronic conductors (MIECs) have been hampered by the paramagnetic behavior of these systems. Here we report high-resolution $\mathrm{<mrow\; data-mjx-texclass="ORD">17</mrow>}$O (I = 5/2) solid-state NMR spectra of the mixed-conducting solid oxide fuel cell (SOFC) cathode material La$2$NiO, a paramagnetic transition-metal oxide. Three distinct oxygen environments (equatorial, axial, and interstitial) can be assigned on the basis of hyperfine (Fermi contact) shifts and quadrupolar nutation behavior, aided by results from periodic DFT calculations. Distinct structural distortions among the axial sites, arising from the nonstoichiometric incorporation of interstitial oxygen, can be resolved by advanced magic angle turning and phase-adjusted sideband separation (MATPASS) NMR experiments. Finally, variable-temperature spectra reveal the onset of rapid interstitial oxide motion and exchange with axial sites at ∼130 °C, associated with the reported orthorhombic-to-tetragonal phase transition of La$2$NiO. From the variable-temperature spectra, we develop a model of oxide-ion dynamics on the spectral time scale that accounts for motional differences of all distinct oxygen sites. Though we treat La$2$NiO as a model system for a combined paramagnetic $\mathrm{<mrow\; data-mjx-texclass="ORD">17</mrow>}$O NMR and DFT methodology, the approach presented herein should prove applicable to MIECs and other functionally important paramagnetic oxides.