Angle-resolved photoelectron spectra, resulting from the strong-field ionization of atoms or molecules, carry a rich amount of information on ionization pathways, electron dynamics, and the target structure. We have investigated angle-resolved photoelectron spectra arising from the nonresonant ionization of xenon Rydberg atoms in the multiphoton regime, using intense midinfrared radiation from a free-electron laser. The experimental data reveal a rich oscillatory structure in the low-order above-threshold ionization region. By performing quantum-mechanical and semiclassical calculations, the observed oscillations could be well reproduced and explained by both a multiphoton absorption picture as by a model invoking electron wave-packet interferences. Furthermore, we demonstrate that the shape and orientation of the initial Rydberg state leaves its own fingerprint on the final angular distribution.