Can a stoichiometric mixture of oxygen and methane exist as a liquid at standard pressure and some (low) temperature?
There's a NASA report that looks into this: "ON THE SOLUBILITIES AND RATES OF SOLUTION OF GASES IN LIQUID METHANE", Hibbard and Evans, 1968 and concludes that such mixtures are possible.

Starting on page 8:


  Figure 5(a) presents the curves for oxygen, argon, carbon monoxide,
  and nitrogen. Also shown are the two experimental values for nitrogen.
  Agreement is excellent at 99.83K and good at 110.9K. The curves for
  these gases show that solubility should decrease with increasing
  temperature and the nitrogen data confirm this. This figure shows the
  mole fraction solubility of oxygen to be 1.0 at 90K. This means that
  oxygen, which has a normal boiling temperature of 90.1K would
  continuously condense in, and be miscible in all proportions, with
  liquid methane at 90K. This is confirmed by reference 11 where, in a
  study of the solubility of methane in liquid oxygen, it was concluded
  that these formed a near-ideal solution at -297 F (90K)


(emphasis added) Reference 11 mentioned in there is "Hydrocarbon-Oxygen Systems Solubility", McKinley and Wang, 1960 (unfortunately paywalled) which also has interesting discussion of the stability (i.e. presence or absence of a tendency to explode) of various mixtures.

Figure 5 is reproduced below. Note how the solubility of oxygen rises rapidly as temperature drops.