We discuss the X-ray properties of 49 local (z < 0.035) Seyfert 2 galaxies with HST/WFC2 high-resolution optical coverage. It includes the results of 26 still unpublished Chandra and XMM-Newton observations, which yield 25 (22) new X-ray detections in the 0.5-2 keV (2-10 keV) energy band. Our sample covers a range in the 2-10 keV observed flux, F 2−10 , from 3 × 10 −11 to 6 × 10 −15 erg cm −2 s −1 . The percentage of objects that are likely obscured by Compton-thick matter (column density, N H ≥ σ −1 t 1.6 × 10 24 cm −2 ) is 50%, and reaches 80% for log (F 2−10 ) < 12.3. Hence, K α fluorescent iron lines with large Equivalent Width (EW > 0.6 keV) are common in our sample (6 new detections at a confidence level ≥2σ). They are explained as due to reflection off the illuminated side of optically thick material. We confirm a correlation between the presence of a ∼100-pc scale nuclear dust in the WFC2 images and Compton-thin obscuration. We interpret this correlation as due to the large covering fraction of gas associated with the dust lanes. The X-ray spectra of highly obscured AGN invariably present a prominent soft excess emission above the extrapolation of the hard X-ray component. This soft component can account for a very large fraction of the overall X-ray energy budget. As this component is generally unobscured -and therefore likely produced in extended gas structures -it may lead to a severe underestimation of the nuclear obscuration in z ∼ 1 absorbed AGN, if standard X-ray colors are used to classify them. As a by-product of our study, we report the discovery of a soft X-ray, luminous ( 7 × 10 40 erg s −1 ) halo embedding the interacting galaxy pair Mkn 266.