We present results from a quantum and semiclassical theoretical study of the rho _xy and rho _xx resistivities of a high mobility 2D electron gas in the presence of a dilute random distribution of tubes with magnetic flux Phi and radius R, for arbitrary values of k_fR and F=e Phi /h. We report on novel Aharonov-Bohm-type oscillations in rho _xy and rho _xx, related to degenerate quantum flux tube resonances, that satisfy the selection rule (k_fR)²=4F(n+1/2), with n an integer. We discuss possible experimental conditions where these oscillations may be observed.