My ship has a fixed volume, but my crew count can range from 1 to 8 and include various species. Do either of those two factors influence the rate of oxygen consumption?
TL;DR. --> No. The rate is fixed.
For Science! --> I ran a series of tests, each iteration tracking the amount of time necessary to go from 100% oxygen to 25% oxygen with all internal doors open. I stopped here to avoid damaging my crew's health and thereby requiring time in sickbay before the next iteration began.
Results were as follows:
As you can see, from one crew to four the oxygen depletion rate remains constant. The rate is also not affected by Mantis or Zoltan biological distinctiveness.
Thus, one must recommend the immediate cessation of emergency crew execution measures intending to reduce oxygen depletion as this approach is demonstrably ineffective.