I understand that this must go hand-in-hand with the exothermic reaction that it is -- something to do with hydrogen bonding (must be more favorable) -- but why? Why is MeOH H-bonding with H20 molecules better than with other MeOH molecules? An increase in entropy doesn't seem realistic given the negative volume change... All very confusing, if you ask me!

First, the mixing of methanol with water is observably exothermic, that is, the enthalpy change is negative (DH < 0). The problem is that the enthalpy change is favorable for mixing almost any liquid with water! This is because water can almost always form stronger intermolecular attractions, even with non-polar molecules, than the other molecules can form with themselves.

A large enough, negative DH will overcome a reduction in entropy every time, and as you say, the reduction in volume leads us to suspect that DS < 0.

But entropy typically controls mixing, and therefore I believe that in this case - as with other miscible liquids - the net entropy of mixing is favorable, that is, DS > 0. Here's a hand-waving explanation:

Ahem.

1. Mixing any two different ensembles of molecules will increase the entropy because a random mixture of water and methanol (or whatever) will have higher entropy than water and methanol (or whatever), separated.

2. However, in order to force different molecules in between the water molecules, you must break hydrogen-bonded networks, forcing them to re-form with cavities for the foreign molecules. This strongly decreases the entropy because the water is now in a more ordered state.

3. If the foreign molecule is able to form hydrogen bonds, a more random network (similar to that in pure water) is able to form; this strongly mitigates the entropy decrease in (2).

4. Notice that for long-chain alcohols like n-butanol or n-hexanol, the non-polar chain forces the formation of larger cavities in the water than can be compensated for by hydrogen-bonding with the alcohol's hydroxyl group, so that long-chain alcohols are less soluble (or even insoluble) in water.

Reference:

T.P. Silverstein, "The real reason oil and water don't mix," Journal of Chemical Education, 75(1), 116-118 (1998).

As for the volume change, I suspect that's because of the fact that methanol is not able to form three hydrogen bonds the way a molecule of water is. This might result in a slightly less open and structured H-bonding network, which would both increase the entropy and decrease the volume. But this is just a guess!