To get insight into the nature of the ionized gas in the nuclear region of LINERs, we performed a study of HST Hα imaging of 32 LINERs. The main conclusion from this analysis is that, for the large majority of LINERs (84%), an unresolved nuclear source has been identified along with extended emission with equivalent sizes ranging from a few tens to a few hundredths of parsecs. Their morphologies do not appear to be homogeneous, since they are grouped into three classes: nuclear outflow candidates (42%), core-halo morphologies (25%), and nuclear spiral disks (14%). Clumpy structures reminiscent of young stellar clusters are not a common property of LINERs. The remaining five galaxies are too dusty to allow a clear view of the ionized gas distribution. A size-luminosity relation was found between the equivalent radius of the Hα emission and the (2-10 keV) X-ray luminosities. Both ionized gas morphologies and the size-luminosity relation are indistinguishable from those of low-luminosity Seyferts, suggesting the same origin for the NLR of LINERs and Seyferts. A relation between soft X-rays and ionized gas has also been suggested for the first time in LINERs. From multiwavelength data, only four out of the 32 LINERs show no evidence of the AGN nature of their nuclear sources from multiwavelength data, but extremely obscured AGNs cannot be discarded given the Compton-thick signatures of their X-ray emission. For the confirmed AGN LINERs, their Hα imaging favour core-halo and outflow morphologies (65% of the cases). Finally, their calculated Eddington ratios show that our LINER sources radiate in the sub-Eddington regime, with core-halo systems having on average higher Eddington ratios than do outflow candidates. Appendix and Figs. 2 and 6 are only available in electronic form at http://www.aanda.org