The change of distance between individual graphene oxide sheets due to swelling is the key parameter to explain and predict permeation of multilayered graphene oxide (GO) membranes by various solvents and solutions. In situ synchrotron X-ray diffraction study shows that swelling properties of GO membranes are distinctly different compared to precursor graphite oxide powder samples. Intercalation of liquid dioxolane, acetonitrile, acetone, and chloroform into the GO membrane structure occurs with maximum one monolayer insertion (Type I), in contrast with insertion of 2-3 layers of these solvents into the graphite oxide structure. However, the structure of GO membranes expands in liquid DMSO and DMF solvents similarly to precursor graphite oxide (Type II). It can be expected that Type II solvents will permeate GO membranes significantly faster compared to Type I solvents. The membranes are found to be stable in aqueous solutions of acidic and neutral salts, but dissolve slowly in some basic solutions of certain concentrations, e.g. in NaOH, NaHCO3 and LiF. Some larger organic molecules, alkylamines and alkylammonium cations are found to intercalate and expand the lattice of GO membranes significantly, e.g. up to ∼35 Å in octadecylamine/methanol solution. Intercalation of solutes into the GO structure is one of the limiting factors for nano-filtration of certain molecules but it also allows modification of the inter-layer distance of GO membranes and tuning of their permeation properties. For example, GO membranes functionalized with alkylammonium cations are hydrophobized and they swell in non-polar solvents.