If you properly fastened your blowoff tube and put the other end in a jar/bottle of sanitzer, then there's no way oxygen got into your beer. It's an airlock, just like a 3 piece or S-shaped airlock with sanitizer in it. Without any other information, I don't think anyone can tell you why your beer tastes bad, but I'd bet it has far more to do with fermentation temps (just hazzarding a guess since I don't have anything else to go off of) then anything else.
Every beer I've ruined (it's a relative term, but I don't hesitate to throw out a bad batch personally, I didn't start brewing to drink beer that's worse then what I can get at the store) has been because I pitched too warm, or fermented too warm..or in one case, I harvested some yeast from a bottle of commercial brew that didn't work out so well.