Why does light travel as waves? Why does light travel as waves instead of say just a straight line? What are the forces that make a light photon travel in a wavelike pattern?
 A: Your wording suggests a few misconceptions:


*

*It seems you are thinking of light as having a corpuscolar nature (nothing wrong with that, you are in good company).
Well it turns out that things just do not work that way.
Phenomena like diffraction (to name one) tell us that we cannot describe the behaviour of light thinking of it as composed by (classical) particles.$^\dagger$

*When we say that "light is composed of oscillating electromagnetic waves", we do not mean that some physical entity that we call "light" is literally going up and down in space. What oscillate are the electric and magnetic fields composing the electromagnetic field.
And when saying that an electrical/magnetic field oscillates we mean that the intensity of that field is going up and down in some complicated way at every point in space. This has nothing to do with actual motion induced by some force.

$^\dagger$ It is probably mandatory at this point to point out that light can't be described as "just" electromagnetic waves either.
It has in fact a quantum mechanical nature, which means that it can be both wave-like and particle-like, depending on what you want to measure.
The double slit experiment is the canonical example of this.
If you still wonder as to why does nature work this way, I suggest you this Phys.SE question regarding the Why vs How issue in physics, and of course the classical Feynman's video.
A: There's a few things to disentangle in this question. Let's talk about photons first. It is not true that a "light photon" travels in a wavelike pattern. If you talk about light in terms of photons the (basic) picture you get is light as billiard balls, moving in straight lines. This is how ray tracing and its ilk work, because (in many situations) you can indeed model light as traveling in straight lines.
Now, if that's true, why do we talk about light waves? The reason is because there's another way to look at light, from the perspective of electromagnetism. In EM, we discover that changing electric fields produce magnetic fields, and vice versa. So imagine you have an electric field that is changing, and the rate at which it changes, is also changing. That E-field generates a magnetic field next to it, and because the E-field isn't changing constantly, that magnetic field itself is changing. Which means next to the magnetic field, an E-field is generated, which generates a magnetic field, etc. You can perhaps imagine how this would produce a wave, as the electromagnetic disturbance in one place gets passed along to other places. The wave theory of light is appropriate to use when you need to talk about interference--light can "get in its own way" in some sense, and this can't be described in terms of light rays and billiard ball photons.
The full reconciliation here depends on quantum mechanics, but what it comes down to is that a proper combination of waves appears to be localized into a wave packet. This "wave packet" looks like a single particle, but is in fact somewhat smeared-out, if that makes sense. If you were far away and not able to measure better, it'd look like a single particle--which is why it sometimes does.
