Oxygen abundances have been derived in a sample of very metal-poor stars using the O I triplet at λλ7771-5 Å and OH lines in the near UV. A detailed NLTE analysis of iron lines has been carried out for one of the observed stars, BD +23°3130, providing consistent values of effective temperature and surface gravity that are in very good agreement with independent estimates from the infrared flux method and Hipparcos parallaxes, respectively. These parameters, especially the higher gravity obtained with respect to previous analyses, reduce the discrepancies claimed between the oxygen abundances determined from OH, O I triplet and [O I] λ6300 Å lines, and give consistent abundances to within 0.16 dex for BD +23°3130 ([Fe/H]NLTE = -2.43). The oxygen abundances derived for this new sample confirm previous findings for a progressive linear increase in the oxygen-to-iron ratio with a slope -0.33±0.02 (including NLTE corrections to the iron abundances for all the stars considered) from solar metallicity to [Fe/H]~ -3, and [O/Fe] values as high as ~1.1 for stars with [Fe/H]<~ -2.5. These results can be interpreted as evidence for oxygen overproduction in the very early epoch of the formation of the Galactic halo, possibly associated with supernova events with very massive progenitor stars.