According to Chambers English Dictionary, can mean 'forgetful; apt to forget; raptly or absent-mindedly unaware; causing, or associated with, forgetfulness, forgotten.'
When it is used to mean "raptly or absent-mindedly unaware" it can be accompanied by eitherof or to. I suppose it is up to whichever the user feels most comfortable with.
Personally, I would tend to use "oblivious of" if the person had no knowledge of something which they had no way to be aware of..... "Sam was walking along the tracks completely oblivious of the train approaching from behind him" ... but I would use "oblivious to" if the person had knowledge but was choosing to totally ignore it.... "Sam dashed across the tracks to snatch the baby from in front of the train, completely oblivious to the danger in which he was putting himself".
So I think what I'm saying is that if the person is "absent-mindedly" involved I'd use "oblivious of" and if they're "raptly" engaged in something else, then I'd use "oblivious to".