Nonequilibrium properties of oxygen ordering in high-Tc superconductors of the Y-Ba-Cu-O type are studied via computer simulation of an anisotropic two-dimensional lattice-gas model in which the ordering processes are controlled by diffusion across the sample edges. With a view to designing optimal annealing strategies, various quenches and annealing schedules through the phase diagram are investigated. The ordering kinetics and the grain morphology are found to have a characteristic dependence on the thermal treatment of the system.