(abridged) We have investigated 136 Chandra extragalactic sources without broad optical emission lines, including 93 galaxies with narrow emission lines (NELG) and 43 with only absorption lines (ALG). Based on fx/fo, Lx, X-ray spectral hardness and optical emission line diagnostics, we have conservatively classified 36 normal galaxies (20 spirals and 16 ellipticals) and 71 AGNs. We found no statistically significant evolution in Lx/LB, within the limited z range. We have built log(N)-log(S), after correcting for completeness based on a series of simulations. The best-fit slope is -1.5 for both S and B energy bands, which is considerably steeper than that of the AGN-dominated cosmic background sources, but slightly flatter than the previous estimate, indicating normal galaxies will not exceed the AGN population until fx ~ 2 x 10-18 erg s-1 cm-2 (a factor of ~5 lower than the previous estimate). A group of NELGs appear to be heavily obscured in X-rays, i.e., a typical type 2 AGN. After correcting for intrinsic absorption, their X-ray luminosities could be Lx > 10^44 erg s-1, making them type 2 quasar candidates. While most X-ray luminous ALGs (XBONG - X-ray bright, optically normal galaxy candidates) do not appear to be significantly absorbed, we found two heavily obscured objects, which could be as luminous as an unobscured broad-line quasar. Among 43 ALGs, we found two E+A galaxy candidates with strong Balmer absorption lines, but no [OII] line. The X-ray spectra of both galaxies are soft and one of them has a nearby close companion galaxy, supporting the merger/interaction scenario rather than the dusty starburst hypothesis.
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