We discuss results of a multiwavelength study of a sample of ~70 radio galaxies, selected in the soft gamma-ray band from INTEGRAL and Swift/BAT catalogues (Bassani et al. 2016), focusing on the X-ray view. This ongoing study is aimed at characterizing for the first time the broad-band emission of a statistically significant sample of radio galaxies, thus constraining the accretion/ejection mechanisms at play in AGNs. The sample contains a significantly larger fraction of giant radio galaxies (linear size > 0.7 Mpc) than typically found in radio surveys; a talk focused on the radio properties of these peculiar objects is also proposed at this meeting (Bruni et al.). Concerning the X-ray absorption properties of the whole sample (Panessa et al. 2016), an intriguing result is the lack of heavily absorbed (Compton-thick) sources, which could hint for a discrepancy between the average absorption properties of radio-loud and radio-quiet AGNs. We also study the relation between X-ray absorption and 21 cm HI absorption, finding a higher probability of 21 cm detection among X-ray absorbed sources. This might in turn suggest that at least part of the X-ray obscuration is due to atomic hydrogen seen at radio frequencies, and that could reside at distances larger than the classical pc-scale torus.