To be honest, this is a very tricky question if you weren't given the pKa values.
But if I had seen this problem on an exam, I would definitely eliminate CH3ONa and NaNH2 first because I know that CH3OH and NH3 are definitely less acidic than CH4, their corresponding conjugate acids. Now let's look at CH3MgBr and CH3Li; this time they have the same conjugate acids, CH4. To decide which one is more acidic, you would have to compare the negative charge on each of the CH3-. You can't decide this unless you look at the positive character of their counterparts: MgBr and Li. Which metal has a higher positive charge? If you were given a periodic table with electronegativity values, you would know that Li is more electropositive than Mg, but you can't decide yet because although Mg is more electronegative, it is next to an electronegative Br which polarizes the Mg making it more electropositive. But even with this information, if you didn't know that the polarization of Br on Mg is greater than the electropositivity of the metals you would probably still be stuck.
Just my opinion on this problem, maybe someone has a better explanation.