We study the effect of crystal superstructures produced by orientational ordering of the ReO4 and ClO4 anions in the quasi-one-dimensional organic conductors, (TMTSF)(2)ReO4 and (TMTSF)(2)ClO4, on the angular magnetoresistance oscillations observed in these materials. Folding of the Brillouin zone due to anion ordering generates effective tunneling amplitudes between distant chains. These amplitudes cause multiple peaks in interlayer conductivity for the magnetic-field orientations along the rational crystallographic directions (the Lebed magic angles). Different wave vectors of the anion ordering in (TMTSF)(2)ReO4 and (TMTSF)(2)ClO4 result in the odd and even Lebed angles, as observed experimentally. When a strong magnetic field is applied parallel to the layers and perpendicular to the chains and exceeds a certain threshold, the interlayer tunneling between different branches of the folded electron spectrum becomes possible, and interlayer conductivity should increase sharply. This effect can be utilized to probe the anion ordering gaps in (TMTSF)(2)ClO4 and (TMTSF)(2)ReO4. An application of this effect to kappa-(ET)(2)Cu(NCS)(2) is also briefly discussed.