We present a field theoretic renormalization group study for the critical behaviour of a uniformly driven diffusive system with quenched disorder, which is modelled by different kinds of potential barriers between sites. Due to their symmetry properties, these different realizations of the random potential barriers lead to three different models for the phase transition to transverse order and to one model for the phase transition to longitudinal order all belonging to distinct universality classes. In these four models that have different upper critical dimensions dc we find the critical scaling behaviour of the vertex functions in spatial dimensions d < dc. Its deviation from purely diffusive behaviour is characterized by the anomaly–exponent η that we calculate at first and second order, respectively in ǫ = dc − d. In each model η turns out to be positive which means superdiffusive spread of density fluctuations in the driving force direction. 1 1