Thirty-seven isotopically highly anomalous presolar Al2O3 grains and one presolar MgAl2O4 grain from a separate of the Tieschitz H3.6 ordinary chondrite were identified out of 17,000 isotopically normal refractory oxide grains by an automatic 16O/18O low mass resolution ion-imaging mapping technique in the ion microprobe. Eight additional presolar Al2O3 grains were found by high mass resolution ion probe measurements of all three stable O isotopes in individual grains, including several that would have been missed by the ion-imaging search. Forty-five of the grains were analyzed for their 16O/17O and 16O/18O ratios. Twenty-four grains were also analyzed for Al-Mg and 17 of them have large excesses of 26Mg, attributable to the radioactive decay of 26Al. The highly anomalous isotopic composition of the grains is evidence for their presolar, stellar origin.The 46 oxide grains of this study together with 42 previously identified presolar grains were divided into four groups. These groups most likely comprise grains from distinct types of stellar sources. Group 1 grains have 17O excesses and moderate 18O depletions, relative to solar, and many of them exhibit 26Mg excesses as well. Group 2 grains have 17O excesses, large 18O depletions, and high inferred 26Al/27Al ratios. Group 3 grains have solar or higher 16O/17O and 16O/18O ratios. Group 4 grains have 17O and 18O enrichments. One Al2O3 grain of this study, T54, has an 16O/17O ratio of 71, lower than any previously observed, and 16O/18O much greater than the solar value. The O-isotopic compositions of Group 1 and Group 3 grains are consistent with an origin in O-rich red giant stars, which have undergone the first dredge-up. The range of O-isotopic ratios of these groups requires multiple stellar sources of different masses and initial isotopic compositions and is well explained by a combination of Galactic chemical evolution and first dredge-up models. The inferred 26Al/27Al ratios of many of these grains indicate that they formed in thermally pulsing asymptotic branch (TP-AGB) stars that had undergone the third dredge-up. Group 2 grains probably formed in low-mass AGB stars as well, and their substantial 18O depletions are the likely result of ``extra'' mixing (cool bottom processing). The origin of the 18O enrichments in Group 4 grains is unknown, but it might be due to initial compositional differences of the stellar sources or to unusual third dredge-up in low-mass AGB stars. The highly 17O-enriched grain T54 could have formed in an AGB star undergoing hot bottom burning or in a massive star in the Of-WN phase. O-rich circumstellar dust seems to be underrepresented in meteorites, relative to C-rich. Explanations include the possibility that most O-rich stardust grains are silicates and have been destroyed either in the laboratory or in nature and the possibility that presolar Al2O3 has a finer grain size distribution than SiC and graphite.