Current-voltage characteristics of few-layer graphene structures (FLGS) obtained by plasma-assisted electrochemical exfoliation of graphite in Na2SO4 solution were measured. FLGS are shown to possess electronic conductivity, which indicates the predominant functionalization of the edges of graphene planes and the preservation of the structure of basal planes in obtained nanostructures as in the source graphite. The effect of humidity on the conductivity of FLGS films was studied. The resistance of films was found to increase with an increase in the relative humidity of the environment due to the shielding of FLGS flakes by a film of water. The effect of different solvents on the current-voltage characteristics of FLGS was analyzed. The conductivity of films significantly decreased in vapors of polar protic solvents, while there was a minor effect of nonpolar aprotic solvents on the conductivity of FLGS films.