Order of stability of substituted benzyl carbanion
I'm not a chemist, but I doubt whether the mesomeric effect is "more in case I than in III" as you put it. 

I'm under the impression that the mesomeric effects (alone) in both cases activate the benzene ring to the same extent (If you try drawing the resonance structures, you'd probably feel the same way).

However, I suppose in case I, the minor $-I$ effect of the $\ce{-OCH3}$ group makes I slightly more stable than III (because the negative charge is somewhat diminished).

So to me, $\mathrm{II &gt; I &gt; III}$ looks about right.