We present a detailed theoretical study on nonlinear transport and optical properties in three-dimensional electron gases 3DEG's subjected to intense terahertz THz electromagnetic radiation fields. The steady-state electronic transition rate induced by electron-photon-phonon interactions in a 3DEG system has been derived by using an approach from which the effects of multiphoton processes can be easily included. By solving the momentum- and energy-balance equations based on a steady-state Boltzmann equation, where electron interactions with LO phonons are taken into account, we have investigated the dependence of electron temperature, relaxation time, mobility, multiphoton absorption and emission, and photon-assisted LO-phonon emission on the intensity and frequency of the THz radiation fields. A number of important and distinctive transport and optical phenomena have been observed and predicted theoretically. These results are pertinent to transport measurements in the presence of a radiation field and to the application of recently developed far-infrared laser sources such as free-electron lasers.