We present a study of the radio continuum properties of two luminous/ultraluminous infrared galaxy samples: the OH megamaser (OHM) sample (74 objects) and the control sample (128 objects) without detected maser emission. We carried out pilot observations for 140 objects with the radio telescope RATAN-600 at 1.2, 2.3, 4.7, 8.2, 11.2, and 22.3GHz in 2019-2021. The OHM sample has two times more flat-spectrum sources (32 per cent) than the control sample. Steep radio spectra prevail in both samples. The median spectral index at 4.7GHz {alpha}_4.7_=-0.59 for the OHM sample, and {alpha}_4.7_=-0.71 for the non-OHM galaxies. We confirm a tight correlation of the far-infrared (FIR) and radio luminosities for the OHM sample. We found correlations between isotropic OH line luminosity L_OH_ and the spectral index {alpha}_4.7_ ({rho}=0.26, p-val.=0.04) and between L_OH_ and radio luminosity P_1.4_ ({rho}=0.35, p-val.=0.005). Reviewing subsamples of masers powered by active galactic nuclei (AGNs) and star formation revealed insignificant differences for their FIR and radio properties. None the less, AGN-powered galaxies exhibit larger scatter in a range of parameters and their standard deviations. The similarities in the radio and FIR properties in the two samples are presumably caused by the presence of a significant amount of AGN sources in both samples (47 and 30 per cent in the OHM and control samples) and/or possibly by the presence of undetected OH emission sources in the control sample.