Photons are certainly particles, but I don't recall Feynman ever saying that they don't travel in waves. Photons are waves AND particles, just like electrons and everything else; their "particle" properties just manifest themselves in different ways from their "wave" properties. [Editor: The wave/particle duality is one of the hardest concepts to visualize in modern physics. Most physicists even have trouble with it. In fact, you simply cannot comprehend it with common sense. It makes no sense in our macroscopic human-scaled world. It only works at the unimaginably small level of atoms and subatomic particles. The only way it can be understood is with mathematics, which explains it beautifully. But the math is too hard to understand unless you have a few university level physics courses. And even then, it's not that easy.]

Your next assertion is correct: the electromagnetic spectrum IS the spectrum of photon energies, and all photons travel at the same speed (c) in vacuum, regardless of their energy.

Now to your real question: what is the energy of a photon? The rigourous answer is, "h nu" -- where "h" is Planck's constant, a universal constant with units of energy times time and a numerical value of about 6.626 x 10^{-34} J-s ( or 0.--insert 34 zeros--6626, pretty small!) and "nu" is the photon's frequency in Hz.

Thus are wedded the "particle" property of a quantized energy (the quanta of light can be called "photons" for this very reason) and the "wave" property of frequency (which goes with wavelength -- the product of the two being the speed of propagation, c).

It gets more interesting when we start talking about the frequency of an electron, which is (nonrelativistically) its kinetic energy divided by Planck's constant. But first you need to get comfortable with the idea of a wave (light) having this particle property (quantized energy), if you can. If it gives you trouble, you're not alone. Anyone who claims this makes perfect sense on the first try is either lying or missing the point.