This paper has two parts: one about observational constraints related to the empirical differential oxygen abundance distribution (EDOD), and the other about inhomogeneous models of chemical evolution, in particular the theoretical differential oxygen abundance distribution (TDOD). In the first part, the EDOD is deduced from subsamples related to two different samples involving (i) N=532 solar neighbourhood (SN) stars within the range, -1.5<[Fe/H]<0.5, for which the oxygen abundance has been determined both in presence and in absence of the local thermodynamical equilibrium (LTE) approximation (Ramirez et al. in Astron. Astrophys. 465:271, 2007); and (ii) N=64 SN thick disk, SN thin disk, and bulge K-giant stars within the range, -1.7<[Fe/H]<0.5, for which the oxygen abundance has been determined (Melendez et al. in Astron. Astrophys. 484:L21, 2008). A comparison is made with previous results implying use of [O/H]-[Fe/H] empirical relations (Caimmi in Astron. Nachr. 322:241, 2001b; New Astron. 12:289, 2007) related to (iii) 372 SN halo subdwarfs (Ryan and Norris in Astron. J. 101:1865, 1991); and (iv) 268 K-giant bulge stars (Sadler et al. in Astron. J. 112:171, 1996). The EDOD of the SN thick + thin disk is determined by weighting the mass, for assumed SN thick to thin disk mass ratio within the range, 0.1-0.9. In the second part, inhomogeneous models of chemical evolution for the SN thick disk, the SN thin disk, the SN thick + thin disk, the SN halo, and the bulge, are computed assuming the instantaneous recycling approximation. The EDOD data are fitted, to an acceptable extent, by their TDOD counterparts with the exception of the thin or thick + thin disk, where two additional restrictions are needed: (i) still undetected, low-oxygen abundance thin disk stars exist, and (ii) a single oxygen overabundant star is removed from a thin disk subsample. In any case, the (assumed power-law) stellar initial mass function (IMF) is universal but gas can be inhibited from, or enhanced in, forming stars at different rates with respect to a selected reference case. Models involving a strictly universal IMF (i.e. gas neither inhibited from, nor enhanced in, forming stars with respect to a selected reference case) can also reproduce the data to an acceptable extent. Our main conclusions are (1) different models are necessary to fit the (incomplete) halo sample, which is consistent with the idea of two distinct halo components: an inner, flattened halo in slow prograde rotation, and an outer, spherical halo in net retrograde rotation (Carollo et al. in Nature 450:1020, 2007); (2) the oxygen enrichment within the inner SN halo, the SN thick disk, and the bulge, was similar and coeval within the same metallicity range, ...