We theoretically investigate the effects of strong couplings in resonant Auger processes under the combination of strong resonant x-ray and nearly resonant optical pulses. The x-ray field couples the ground state with a core-excited state, while the optical field couples the core-excited state with another core-excited state of opposite parity. The Auger electron spectrum changes its shape as the intensities of the x-ray and/or optical fields increase, and at sufficiently high intensities we observe that the splitting, which is induced by the optical field, is superposed on the asymmetric splitting induced by the x-ray field in the Auger electron spectra. The asymmetric splitting itself, which is induced by the strong x-ray pulse, is persistent but modified due to the presence of the strong optical field. Moreover, through the systematic study by including or excluding the individual photoionization processes from the core-excited states and the direct photoionizaton process from the ground state, we clarify the contribution of the respective processes to the total electron yield and the Auger electron spectra. These results show that we can manipulate the resonant Auger processes through the introduction of the second core-excited state and the strong optical field.