  (Abridged) We present the results of the photometric and spectroscopic
identification of 110 hard X-ray selected sources (6e-15<F(2-10 keV)<4e-14 cgs)
from 5 additional XMM-Newton fields, nearly doubling the original HELLAS2XMM
sample. We spectroscopically identified 59 new sources, bringing the
completeness of the full HELLAS2XMM sample to ~70%. We found optical
counterparts for 214 out of the 232 X-ray sources of the full sample down to
R~25. We measure the flux and luminosity of the [OIII](5007) emission line for
59 such sources. Results. We use the full HELLAS2XMM and the CDF samples to
estimate the LogN-LogS and the obscured QSO surface densities down to F(2-10
keV)~1e-14 and 1e-15 cgs. At these flux limits the fraction of X-ray selected
obscured and unobscured QSO turns out to be similar. Since X-ray selection
misses most Compton thick AGN, the number of obscured QSO may well outnumber
that of unobscured QSOs. We find that hard X-ray selected AGNs with detected
[OIII] emission span a wide range of L(2-10 keV)/L[OIII] with a median higher
than that of optically selected AGNs, suggesting that optically selected
samples are at least partly incomplete, and/or [OIII] emission is not a perfect
isotropic indicator of the nuclear power. Differently from narrow-line AGNs in
the same z interval, the 7 XBONGs candidates in the sample have L(2-10
keV)/L[OIII]> 1000, while their Lx, L(R) and Nh are similar. This suggests that
while the central engine of narrow-line AGNs and XBONGs looks similar, the
narrow-line region in XBONGs could be strongly inhibited or obscured.
