We introduce a self-consistent approach for the description of the nonlinear light propagation in InAs/InGaAs quantum-dot semiconductor optical amplifiers and, using it, numerically analyze the four-wave mixing conversion efficiency in such amplifiers. This approach is based on a delay-differential equation for the optical field propagating through the amplifier and additional equations describing the microscopically calculated charge-carrier dynamics in the quantum-dot states and the surrounding quantum well reservoir. Here, we draw our attention to the studies of the hierarchy of the nonlinear effects involved in the four-wave-mixing processes We observe that the spectral hole burning is the most important effect to drive the four-wave mixing The charge-carrier density pulsation appearing together with the spectral hole burning constitutes the second most important effect, while the charge-carrier heating turned out to be negligible. Furthermore, we found that the four-wave mixing conversion efficiency can be effectively increased when higher device pump current or higher device temperature is used, provided that the frequencies of the injected light sources are adjusted to the temperature-dependent gain maximum.