How does the relative amount of oxidation of different alcohols affect the amount of energy released?
It doesn't have to do with incomplete combustion, as the enthalpy values you've seen reported are for the enthalpy of complete combustion.  

It has to do with the alcohol already being partially oxidized, so there is less energy available for release upon the oxidative process of combustion.  In other words, if a particular carbon atom is already partially oxidized, like in an alcohol, then you can't get as much energy from combustion as compared to a more reduced carbon, like that in a methyl group for example.  

This effect is most pronounced for the low-molecular weight alcohols.  Methanol has 1 oxygen per carbon atom, while ethanol has 0.5 oxygens per carbon atom.  That is a much larger relative difference than there is between a $\ce{C10}$ alcohol and a $\ce{C11}$ alcohol.  In other words, the larger a mono-hydroxy alcohol is, the more it resembles a pure alkane with respect to the enthalpy of combustion.