Aims: We present a detailed and uniform study of oxygen abundance from two different oxygen lines at 6158 Å and 6300 Å in a large sample of solar-type stars. The results are used to check the behaviour of these spectral lines as oxygen abundance indicators and to study the evolution of oxygen in thick and thin disk populations of the Galaxy. Methods: Equivalent width measurements were carried out for the [OI] 6158 Å and OI 6300 Å lines. Local thermodynamic equilibrium (LTE) abundances were obtained from these two lines in 610 and 535 stars, respectively. We were able to measure oxygen abundance from both indicators in 447 stars enabling us for the first time to compare them in a uniform way. Careful error analysis has been performed. Results: We found that oxygen abundances derived from the 6158 Å and 6300 Å lines agree to within 0.1 dex in 58% of the stars in our sample, and this result improves for higher signal-to-noise values. We confirm an oxygen enhancement in stars of the thick disk, as has also been seen for other α-elements. The new oxygen abundances confirm previous findings for a progressive linear rise in the oxygen-to-iron ratio with a slope equal to 0.78 from solar metallicity to [Fe/H] ~ -1. However, the slope we measured is steeper than the one found in previous studies based on the oxygen triplet. Below [Fe/H] = -0.6 our stars show [O/Fe] ratios as high as ~0.8, which can be interpreted as evidence for oxygen overproduction in the Galactic thick disk. These high oxygen abundances do not pose a problem to chemodynamical models since there is a range of parameters that can accommodate our results. Full Tables 2, 3, A.1, and A.2 are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/576/A89