Is there any evidence to suggest that subatomic particles have 3D physiscal size? What I'm asking is do subatomic particles like a proton have a volume or any 3 dimensional size? Or are they just points?  
 A: Protons and neutrons are extended object, being roughly $1\,\mathrm{fm}$ in radius. Give or take a bit, depending on how you want to define their size.
Evidence for this comes in three basic forms: first from scattering experiments in which we bounce other particles off of them (electrons are particularly good for this applications); second from packing experiments (AKA seeing how the size of large nuclei depends on the number of nucleons); and finally the fine details of the hydrogen atomic energy levels (which depend in a small degree on the charge distribution of the proton). However, the second sense depends on measuring the size of the nuclei which comes back to scattering experiments again, so in a sense they are the same.
So, how do the scattering experiments work?
Well, if you are doing electron-proton scattering the interaction is electromagnetic in character. So, for any given electron energy you can calculate the distribution of scattering angles that would result from sending a beam of electron at a proton target (a thin-walled can containing liquid hydrogen in most cases) *under the assumption that the proton was point like.
Then you run this experiment over and over again at different energies and you see that your results agree without your calculation at all energies up to some threshold above which they disagree and you get fewer hard scattering event that you predicted.
Finally you calculate the distance of closest approach for electrons with the threshold energy and you take that as an approximation to the charge radius of the proton.
A: The elementary particles of the Standard model are pointlike. This has been determined by numerous experiments. All other particles except the ones in the table are composites of some of the ones in the table, and these have dimensions that have been measured using scattering experiments to find their form. Here is an answer on how this is done.
