It would be interesting to hear what would happen if you had an emergency oxygen supply, like one of those miniature scuba tanks. How would that change the survival range?
The peak of Mount Everest is about 1/3 atmosphere, and base camp is in about 1/2 atmosphere. This means the partial pressure of oxygen at those locations is about 0.07 and 0.1 atmospheres, respectively. People who have not acclimated to high altitudes (by spending 2 months at base camp) will pass out on the peak (and it still sucks pretty hard even if you're acclimated).
So, it seems like pure oxygen at 0.1 atmosphere should work, although I suspect it'd be hella uncomfortable even without the vacuum, since it'd probably feel like you were trying to blow up the worlds largest balloon while standing on Mount Everest.
But it does let us move on. So you're standing in a vacuum (on the Moon, maybe) sucking on 0.1 atmosphere of pure oxygen. How long can you survive for?
You might need to keep a small amount of lung pressure (say, less than that used to blow up party balloons) to slow the egress of oxygen through the lungs.
The next problem is likely that your lungs catch fire as the O2 concentration builds up in them. One thing at a time though.
Hyperventilating is good for removing CO2 from your blood, which reduces your "I really need to breath" reflex (turns out that is, at least largely, cause by the presence of CO2 rather than the absence of O2). From personal experience I can tell you this can allow you to push yourself further without breathing, but you also run the risk of blacking out because you pushed too far (I don't have experience with that part).