Momentum measures how hard it is to stop an object. While Photons are massless they still have relativistic mass and energy. My question is can something stop photons other than being absorbed by something?
What does momentum mean when talking about massless particles?
Your question is not quite accurate, this because you thinking of Photon as a classical particle (solid ball), but it's not, photon (same as other particles) are quantum particles, thus you should consider particle-wave duality, in other hand, because photon has no mass, it can't move at any speed other than speed of light (In vacuum), otherwise it will not exist.
Finlay, the momentum of massless particle, can be thought of as "amount of motion" , or even more directly, it is related actually not to speed of photon (like in classical physics) but to wave length by the following famous De Broglie relation:
$$ p=\frac{h}{\lambda}$$
Thus there is no sense of saying "stopping a photon" in vacuum, it can exist only in motion and strictly at speed of light, or "absorbed" fully or partially, what will change it's energy/momentum, but not it's speed!
P.S
The situation is more complicated for photons in some media, anyway one can slow down and maybe "even freeze" them.
