To shed light onto the circumnuclear environment of 22 GHz (lambda similar to 1.3 cm) H2O maser galaxies, we have analyzed some of their multiwavelength properties, including the far-infrared luminosity (FIR), the luminosity of the [OIII]lambda 5007 emission line, the nuclear X-ray luminosity, and the equivalent width (EW) of the neutral iron K alpha emission line (EW (K-alpha)). Our statistical analysis includes a total of 85 sources, most of them harboring an active galactic nucleus (AGN). There are strong anticorrelations between EW (K-alpha) and two "optical thickness parameters," i.e., the ratios of the X-ray luminosity versus the presumably more isotropically radiated [OIII] and FIR luminosities. Based on these anticorrelations, a set of quantitative criteria, EW (K-alpha) > 300 eV, L2-10 (keV) < 2 L-[OIII], and L-FIR > 600 L2-10 (keV) can be established for Compton-thick nuclear regions. Eighteen H2O maser galaxies belong to this category. There are no obvious correlations between the EW (K-alpha), the [OIII] luminosity, and the isotropic H2O maser luminosity. When comparing samples of Seyfert 2s with and without detected H2O maser lines, there seem to exist differences in EW (K-alpha) and the fraction of Compton-thick nuclei. This should be studied further. For AGN masers alone, there is no obvious correlation between FIR and H2O maser luminosities. However, including masers associated with star-forming regions, a linear correlation is revealed. Overall, the extragalactic FIR-H2O data agree with the corresponding relation for Galactic maser sources, extrapolated by several orders of magnitude to higher luminosities.