We study the radio variability of galaxies with and without sources of hydroxyl (OH) megamaser radiation based on the continuum radio measurements conducted in 2019-2022 with the radio telescope RATAN-600 at frequencies of 2.3, 4.7, 8.2, and 11.2 GHz. Presumably, radio continuum emission significantly affects the megamaser radiation brightness, therefore, such a characteristic as the variability of radio emission is important for determining the OHM galaxies parameters. With additional data from the literature, the parameters of radio variability on a time scale up to 30 years were estimated. The median values of the variability index for 48 OHM galaxies are in the range $V_{S}=0.08$-$0.17$, and for 30 galaxies without OH emission they are $V_{S}=0.08$-$0.28$. For some individual galaxies in both samples, flux density variations reach 30-50%. These sources either are commonly associated with AGNs or reveal active star formation. Generally, the variability of luminous infrared galaxies with and without OH megamaser emission is moderate and of the same order of magnitude on long time scales. From estimating the spectral energy distribution parameters in a broad frequency range (from MHz to THz), we determined the spectral index below 50 GHz and the color temperatures of dust components for megamaser and control sample galaxies. At a level of $\rho<0.05$, there are no statistically significant differences in the distribution of these parameters for the two samples, as well there are no statistically significant correlations between the dust color temperatures and the variability index or luminosity in the OH line.