Oxidation of UO2 in the nuclear fuel cycle leads to formation of the layered uranium oxides. Here we present DFT simulations of U2O5 and U3O8 using the PBE + U functional to examine their structural, electronic and mechanical properties. We build on previous simulation studies of Amm2 α-U3O8, P21/m β-U3O8 and P62m γ-U3O8 by including C222 α-U3O8, Cmcm β-U3O8 and Pnma δ-U2O5. All materials are predicted to be insulators with no preference for ferromagnetic or antiferromagnetic ordering. We predict δ-U2O5 contains exclusively U5+ ions in an even mixture of distorted octahedral and pentagonal bipyramidal coordination sites. In each U3O8 polymorph modelled we predict U5+ ions in pentagonal bipyramidal coordination and U6+ in octahedral coordination, with no U4+ present. The elastic constants of each phase have been calculated and the bulk modulus is found to be inversely proportional to the volume per uranium ion. Finally, a number of thermodynamic properties are estimated, showing general agreement with available experiments; for example α- and β-U3O8 are predicted to be stable at low temperatures but β-U3O8 and γ-U3O8 dominate at high temperature and high pressure respectively.