Quantum mechanically speaking, light is made up of bosons. Bosons are force carrying particles and are defined as having integer spin numbers (usually 1 or 2). Spin is sort of like a particles's angular momentum. The specific boson that light is made up of is the photon, which carries the electromagnetic force. The electromagenetic force is one force that behaves differently depending on the situation, thus manifesting itself as either the electric force in static situations or the magnetic force in dynamic situations. So if a particle wants to intereact with another particle, both particles emit photons which tell it how to behave (i.e. two particles of opposite charge attracting eachother). If a stream of photons is traveling in space, macroscopically it appears as a beam of light.
In quantum mechanics, all particles have wave properties according to their associated quantum state, including photons. Since atoms are made up of a large number of particles with differing frequencies (quarks, leptons, photons, gluons, gravitons, etc.), it is very difficult to measure these properties. It is much more common to find a stram of photons all with the same wave characteristics (i.e a laser beam), thus it is very easy to measure the frequencies of light.
Mass is a tricky one. Theoretically, massive particals interact with eachother via the graviton, however the quantum theory is very incomplete with this regard. This is one of the most avtive areas of research in physics. According to the standard model, mass is given to particles via the hypothetical Higgs boson through quantum mechanical interactions. Thus only the particles that interact with the Higgs boson are given mass. There is a whole mathematical model which predicts what particles have mass and which do not. Since the photon doesn't interact with the Higgs boson, it does not have mass.
As for momentum, all particles carry momentum because they have energy, not neccessarily because they have mass. According to Newtonian physics, momentum is defined by an inertial mass, however Maxwell's equations show that electromagnetic radiation, and by extension photons, carry moment with them as well. Basically, when photons collide with a surface, they impart some of their energy to the surface in the form of kenetic energy.
Hope this helps.