We present a theoretical investigation of high-frequency electronic noise in field-effect transistors used as detectors of TeraHertz radiation. Calculations are performed using the hydrodynamic-Langevin approach and specialized to the case of InGaAs high-electron mobility transistors. The main physical phenomena associated with the effect of branching of the total current between channel and gate and the appearance of two-dimensional plasma waves are discussed. We demonstrate that thermally excited standing plasma waves originate series of resonant peaks in the corresponding noise spectral densities whose presence can be controlled by the embedding circuit. A significant damping of the high-frequency excess noise is found when the transistor is submitted to a two-lasers optical photo-excitation presenting a beating frequency in the TeraHertz range. Finally, we discuss the dependence of the damping effect, as well as a shift of the resonance peaks from the presence of channel ungated regions.