Effect of the long-range interaction (screened Coulomb and strain-induced interactions) on the structure transformations is investigated in terms of the crystal lattice site diffusion theory for the specific generic case of YBa2Cu3O6+delta oxides. The computer simulation of oxygen ordering has demonstrated that oxygen-induced strain is accommodated by self-organized (110) twins which may strongly affect the crystallographic structure of ordered phases. Twin (110) boundaries and the atomic structures prove to be coupled by the long-range interaction. This interaction results in appearance of 2a0 x 2a0 and 2 square-root 2a0 x 2 square-root 2a0 superstructures. Existence of two types of new aperiodic mesoscopic metastable phases is also predicted. These phases, the secondary tweed and the ''glassy'' state, consist of mesoscale domains of the double-period orthorhombic O(II) phase. These domains belong either to the same orientation variant (the ''glassy'' state) or to two orientation variants (the ''secondary'' tweed structure). Unlike conventional phases, the domains of the mesoscopic phases do not undergo coarsening. It is shown that at the exact stoichiometry of the O(II) phase, delta = 0.5, the ordering produces a conventional ordered O(II) phase whose antiphase domains undergo usual coarsening. The structures and morphologies generated in this computer simulation were reported in many experimental studies.