It looks like there’s some confusion here by what is meant by “oxygen.” The OP seems to be asking about free molecular oxygen, O[sub]2[/sub], and free H[sub]2[/sub]O. Free oxygen we know for a fact is not necessary for life even as we know it, and in fact is toxic to pretty much everything. Some lifeforms have figured out ways of dealing with the toxicity, so mammals are largely hypoxic inside but they carry oxygen around in iron cages (hemoglobin). Probably most microbial life, and thus most life overall, is at best unable to grow in the presence of, and at worst actively and viciously killed by, free oxygen. So in searching for extraterrestrial life, an oxygen atmosphere isn’t seen as a prerequisite for life, but as an extremely strong sign of it. Plus we’d want an oxygen atmosphere there already if we ever wanted to move to that planet.
Compounded oxygen is a bit different; basically chemistry has a large but limited toolbox. I suppose it’s not outright impossible to have some life with an all-metal chemistry, but otherwise you’re going to have nonmetals involved, and the second row of the periodic table has the most abundant and reactive nonmetals: carbon, nitrogen, and oxygen. Oxygen especially is utterly ubiquitous as soon as you go to any environment that isn’t mostly hydrogen and helium. Even if you had some hypothetical silicon-based life, the Earth’s crust has nearly twice as much oxygen as silicon in it by weight, so there’s going to be some oxygen chemistry going on there no matter what.
Water’s a little bit trickier, but as tallcoldone and others have pointed out, it does a bunch of things that we think are necessary for life, and it’s utterly ubiquitous in the universe. If your biochemistry involves both hydrogen and oxygen, water is almost certainly going to be produced at some step. It’s conceivable that life can exist without liquid water, and there would be detectable evidence of life without it (for instance, last I heard the excess of molecular hydrogen in Titan’s atmosphere is “consistent with” the presence of life there, which is to say not even as strong as “evidence for” but at least it leaves the door open a crack) but in general we wouldn’t know if we’d found “life Jim but not as we know it” even if we were looking for it. For the time being, it makes more sense to look for life as we know it rather than speculate about exotic forms of life without having any evidence that it’s possible to begin with.