We utilized the momentum transfer (Q)-dependence of quasi-elastic neutron scattering (QENS) to measure the dynamics of water and ethanol confined in graphene oxide (GO) powder or membranes at different temperatures and in different orientations. We found reduced diffusivities (up to 30% in the case of water) and a depression of dynamic transition temperatures. While water showed near Arrhenius behavior with an almost bulk-like activation barrier in a temperature range of 280-310 K, the diffusivity of ethanol showed little temperature dependence. For both water and ethanol, we found evidence for immobile and mobile fractions of the confined liquid. The mobile fraction exhibited jump diffusion, with a jump length consistent with the expected average spacing of hydroxide groups in the GO surfaces. From anisotropy measurements, we found weak anisotropy in the diffusivity of the mobile species and in the fraction and geometry of immobile species.