Predict Entropy based on the Balanced Equation
Aqueous salts will always have less order than solid salts. There is much less order when ions are floating around in solution than when they are in their rigid lattice structures. This is what I think you are failing to consider. The reaction is not so much:

$$\ce{2Na_{(s)} + 2H2O_{(l)} -&gt; 2NaOH_{(aq)} + H2_{(g)}}$$

But really:

$$\ce{2Na_{(s)} + 2H2O_{(l)} -&gt; 2Na^{+}_{(aq)} +2OH^{-}_{(aq)} + H2_{(g)}}$$

What results from the reaction of 2 atoms of a very structured metal and 2 molecules of liquid water, is 4 aqueous ions that are free to move within the solution, and one molecule of gas. Not only are there now more species present, but they are also in a relatively more free states than before.