As a continuation of a systematic study of reactions relevant to the astrophysical p process, the cross sections of the 74,76Se(p,gamma)75,77Br and 82Se(p,n)82Br reactions have been measured at energies from 1.3 to 3.6 MeV using an activation technique. The results are compared to the predictions of Hauser-Feshbach statistical model calculations using the NON-SMOKER and MOST codes. The sensitivity of the calculations to variations in the optical proton potential and the nuclear level density was studied. Good agreement between theoretical and experimental reaction rates was found for the reactions 74Se(p,gamma)75Br and 82Se(p,n)82Br.