Microwave-radiation induced giant magnetoresistance oscillations recently discovered in highmobility two-dimensional electron systems are analyzed theoretically. Multiphoton-assisted impurity scatterings are shown to be the primary origin of the oscillation. Based on a theory which considers the interaction of electrons with electromagnetic fields and the effect of the cyclotron resonance in Faraday geometry, we are able not only to reproduce the correct period, phase, and the negative resistivity of the main oscillation, but also to predict the secondary peaks and additional maxima and minima observed in the experiments. These peak-valley structures are identified to relate, respectively, to single-, double-, and triple-photon processes.