The spin probe technique was used to study graphite oxide (GO) powders swelled in polar liquids (CH3CN, CH3OH, and H2O) and liquid-free GO membranes (GOM). The nitroxide radicals TEMPO (2,2,6,6-tetramethylpiperidine-N-oxyl) and TEMPOL (4-hydroxy-2,2,6,6-tetramethylpiperidine-N-oxyl) readily penetrated into the interplane space of GO from the solution. Electron paramagnetic resonance (EPR) spectra of these radical probes were sensitive to molecular mobility and orientation ordering within the internal space of GO. The radicals embedded in swelled GO were in two states with different rotational mobilities. The small fraction of radicals located in the interplane space of GO and detected in the broad range of temperatures was in the state of fast rotation, similar to the same radicals dissolved in bulk liquids, thus providing experimental evidence of formation of a liquid-like media within the interplane space of GO. Such mobile media may be responsible for the unusual permeation properties of GOM, which is reported in the literature. Second, less-mobile fraction of radicals was found to be immobilized at the internal surface of GO and was sensitive to phase transformations in the swelled GO structures. The transformations were detected as anomalies at temperature dependences of rotational mobility of radicals. The detected dependence of EPR spectra of probe radicals on orientation of GOM, relative to the direction of magnetic field in the EPR spectrometer, was used for quantitative characterization of orientation alignment of GO planes within the membranes. Such an approach may serve as an elegant method to estimate the relative quality of membranes and other GO-layered structures.