We present the second part of results of the on-going project of searching for and studying eXtremely Metal-Poor (XMP, adopted as those with Z(gas) <~ Zo/30, or with 12+log(O/H) <~ 7.21~dex) very gas-rich blue dwarfs in voids.They were first identified in course of the unbiased study of galaxy population in the nearby Lynx-Cancer void. These very rare and unusual galaxies seem to be the best proxies of so-called Very Young Galaxies (VYGs) defined recently in model simulations by Tweed et al. To date, for 16 preselected void XMP candidates, we obtained with the SAO 6-m telescope (BTA) spectra suitable for determination of O/H. For majority of the observed galaxies, the principal line [OIII]4363 used for the direct classical T_e method of O/H determination, is undetected. Therefore, to estimate O/H, we use a new Strong-lines method by Izotov et al. This appears the most accurate empirical O/H estimator for the range of 12+log(O/H) < 7.4-7.5. For higher O/H objects, we use the semi-empirical method by Izotov and Thuan with our modification accounting for variance of the excitation parameter O32. Six of those 16 candidates are found to be the confident XMP dwarfs. In addition, eight studied galaxies are somewhat less metal-poor, with 12+log(O/H) = 7.24-7.33. They also can fall into the category of VYG candidates. With account of the recently published by us and previously known (9 prototype galaxies) XMP gas-rich void objects, the new findings increase the number of this type galaxies to the total of 19.