We report an experimental study of the edge surface superconductivity and the Hall effect in a Nb thin film Hall device. We show that the previously reported anomalous sign reversal of the Hall resistance across the superconducting-normal transition is due to the edge supercurrent. Large anomalous oscillations between the transverse voltage probes are observed in the field range between Hc2 and Hc3, in both the anti-symmetric (Hall) and symmetric (resistive) channels. These oscillations are extremely sensitive to a small tilting of the edge surface relative to the external magnetic field. We suggest that these oscillations may arise from the Aharonov-Bohm interference of the edge supercurrents.