Oxidation of UO(2) in the nuclear fuel cycle leads to formation of the layered uranium oxides. Here we present DFT simulations of U(2)O(5) and U(3)O(8) using the PBE + U functional to examine their structural, electronic and mechanical properties. We build on previous simulation studies of Amm2 α-U(3)O(8), P2(1)/m β-U(3)O(8) and P6[combining macron]2m γ-U(3)O(8) by including C222 α-U(3)O(8), Cmcm β-U(3)O(8) and Pnma δ-U(2)O(5). All materials are predicted to be insulators with no preference for ferromagnetic or antiferromagnetic ordering. We predict δ-U(2)O(5) contains exclusively U(5+) ions in an even mixture of distorted octahedral and pentagonal bipyramidal coordination sites. In each U(3)O(8) polymorph modelled we predict U(5+) ions in pentagonal bipyramidal coordination and U(6+) in octahedral coordination, with no U(4+) 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-U(3)O(8) are predicted to be stable at low temperatures but β-U(3)O(8) and γ-U(3)O(8) dominate at high temperature and high pressure respectively.