  By using a large highly obscured ($N_{\rm H} > 10^{23}\ \rm cm^{-2}$) AGN
sample (294 sources at $z \sim 0-5$) selected from detailed X-ray spectral
analyses in the deepest Chandra surveys, we explore distributions of these
X-ray sources in various optical/IR/X-ray color-color diagrams and their
host-galaxy properties, aiming at characterizing the nuclear obscuration
environment and the triggering mechanism of highly obscured AGNs. We find that
the refined IRAC color-color diagram fails to identify the majority of X-ray
selected highly obscured AGNs, even for the most luminous sources with ${\rm
log}\,L_{\rm X}\, \rm (erg\ s^{-1}) > 44$. Over 80% of our sources will not be
selected as heavily obscured candidates using the flux ratio of $f_{\rm 24 \mu
m}\, /\,f_R > 1000$ and $R - K > 4.5$ criteria, implying complex origins and
conditions for the obscuring materials that are responsible for the heavy X-ray
obscuration. The average star formation rate of highly obscured AGNs is similar
to that of stellar mass- ($M_*$-) and $z$-controlled normal galaxies, while the
lack of quiescent hosts is observed for the former. Partial correlation
analyses imply that highly obscured AGN activity (traced by $L_{\rm X}$)
appears to be more fundamentally related to $M_*$, and no dependence of $N_{\rm
H}$ on either $M_*$ or SFR is detected. Morphology analyses reveal that 61% of
our sources have a significant disk component, while only 27% of them exhibit
irregular morphological signatures. These findings together point toward a
scenario where secular processes (e.g., galactic-disk instabilities), instead
of mergers, are most probable to be the leading mechanism that triggers
accretion activities of X-ray-selected highly obscured AGNs.
