The HELLAS2XMM survey.VIII. Optical identifications of the extended sample
(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.