We present a detailed theoretical investigation of the radiation induced giantmagnetoresistance oscillations recently discovered in high-mobility two-dimensional electrongas. Electron interactions with impurities, and transverse and longitudinal acousticphonons in GaAs-based heterosystems are considered simultaneously. Multiphoton-assistedimpurity scatterings are shown to be the primary origin of the resistance oscillation.Based on the balance-equation theory developed for magnetotransport in Faradaygeometry, we are able not only to reproduce the observed period, phase and thenegative resistivity of the main oscillations, but also to predict the secondarypeak/valley structures relating to two-photon and three-photon processes. Thedependence of the magnetoresistance oscillation on microwave intensity, the role ofdc bias current and the effect of elevated electron temperature are discussed.Furthermore, we propose that the temperature dependence of the resistance oscillationstems from the growth of the Landau level broadening due to the enhancement ofacoustic phonon scattering with increasing lattice temperature. The calculatedtemperature variation of the oscillation agrees well with experimental observations.