Is there a way to quantify the 'surface area' or simply the shape of organic compounds? I wish to write an investigation into the effects of the shape of organic compounds and the location of the functional groups on the enthalpy of combustion of the organic compounds. Thus, I wonder if there is a way of quantifying these variables, as databases I have looked at do not provide much of an answer.
It is possible to compute the surface area of a molecules, and to compute the surface area of each individual atom in a molecule. These areas depend on the conformation of the molecule. An example of a software that does this is MSMS (http://mgltools.scripps.edu/packages/MSMS).

With respect to the shape, it is possible to categorize molecules in a triangular diagram describing similarity with "rods", "disks" and "spheres" (e.g. http://pubs.acs.org/doi/10.1021/ci300415d). Details about this analysis were published here: http://pubs.acs.org/doi/10.1021/ci025599w.