In principle you could fit a very large number of photons tointo a finite volume but with a limit. Even though photons are waves, they have energy and from general relativity you can only have so much energy in a certain region up to a point where the energy density is so high that the region will collapse into a black hole. At this point the region will be infinitely dense and infinitely small.
So you probably could not fit an infinite number in a finite volume as the energy density will be infinite. This would also apply to fundamental particles as well (assuming they have no well defined volume) since they have mass and therefore energy.
Furthermore, if you were to continually put more photons/matter into it, the "stuff" inside the black hole (given a sufficient length of time) will gradually dissolve by radiating away the energy of the stuff that was there to begin with, once again meaning that no finite region can have infinite photonphotons/particles/matter.
To see more on this last part, click this link for more information about Hawking Radiation.