To add to the Bob's excellent answer (and expand a bit on my comment there), I've found two other potentially interesting papers to peruse.
The first is R.J. Hodges and R.J. Burch, Cryogenics 7 112-113 (1967), titled "The equilibrium distribution of methane between the liquid and vapour phases of oxygen". They note a "very high solubility of methane in liquid oxygen", with a equilibrium distribution coefficient at 93.15K (1.348 atm of O2) of 3.356 (so about 3x more methane in the liquid than in the gas phase). However, they kept the concentration of methane below the lower explosive limit so that it would not, well, explode.
Of perhaps more interest to the OP is R.L. Every and J.O. Thieme, Journal of Spacecraft and Rockets 2(5) 787-789 (1965) titled "Liquid oxygen and liquid methane mixtures as rocket monopropellants". In the introduction the authors note that previous work shows that the liquids are miscible in all proportions above 90K. Their tests show a specific impulse of almost 300 sec, and an exhaust velocity near 6000 fps.
In addition, since "shock sensitivities were reported" in the earlier work, they did some, well, vaguely disturbing experiments (hey, it was the 60's). "Tests were conducted to determine whether violent stirring or agitation, as found in an impeller-type pump, would detonate the mixture", although they didn't have any explosions there. They then went on to quantify the impact sensitivity, dropping a weight onto a stainless steel beaker of different mixtures from increasing heights until an explosion occurred. Impact sensitivities of 20-60 ft-lb were discovered. They also looked at adiabatic compression as a cause of explosion and found the liquid oxygen/methane mixtures were safer than some other things like nitromethane (which really isn't that comforting).
So, it would appear that the idea of using the liquid mixture as a monopropellant isn't totally off the wall, but please do it somewhere far from me...