The properties of a system of charged particles on a 2D lattice, subject to an anisotropic Jahn-Teller-type interaction and 3D Coulomb repulsion, are investigated. In the mean-field approximation without Coulomb interaction, the system displays a phase transition of first order. When the long-range Coulomb interaction is included, Monte Carlo simulations show that the system displays very diverse mesoscopic textures, ranging from spatially disordered pairs to ordered arrays of stripes, or charged clusters, depending only on the ratio of the two interactions (and the particle density). Remarkably, charged objects with an even number of particles are more stable than with an odd number of particles. We suggest that the diverse functional behavior-including superconductivity-observed in oxides can be thought to arise from the self-organization of this type.