We present a study of the arcsecond-scale radio continuum and OH line emission of a sample of known OH megamaser (OHM) galaxies with z ≥ 0.15 using archival Very Large Array (VLA) data and also the results of our pilot Five-hundred-meter Aperture Spherical radio Telescope (FAST) observations of 12 of these OHM galaxies. The arcsecond-scale resolution images show that the OH emission is distributed in one compact structure and is spatially associated with radio continuum emission. Furthermore, nearly all the components we fit are likely smaller than the beam size (∼1.4″), which indicates that the broad OH line profiles of these sources originated from one masing region or that more components are distributed on subarcsecond scales. The radio parameters, including brightness temperature, spectral index, and q-index, show no significant differences with low-redshift OHM galaxies, which have significantly lower OH line luminosities. Because these parameters are indicators of the central power sources (active galactic nucleus, starburst, or both), our results indicate that the presence of a radio active galactic nucleus in the nuclei may not be essential for the formation of OH emission. Over one-third of OHMs in this sample (6 out of 17) show possible variable features that are likely caused by interstellar scintillation due to small angular sizes. We might underestimate this value because these sources are associated with the highest OH line flux densities of this sample. The sources with low OH line flux densities might need observations with higher sensitivity so that the variabilities can be studied. These results support the compact nature of OH maser emission and a starburst origin for the OHMs in our selected sample.