In scattering, how does a particle 'know' which direction it is being illuminated from? In scattering experiments, for example light scattering, the scattering strength from different sized particles is depicted as below.

What I can't understand is: how does a particle know which direction the light is coming from and therefore which direction to bias the scattering (as in the case of large particles)? For instance, if we are just thinking about the electron oscillations, don't they just occur perpendicular to the light source?
So in my example below, I have a particle being illuminated from the left, and one from the right. If we were to look at JUST the electron oscillations inside particle, wouldn't they be doing the exact same thing? So how does the scattered wave seem to 'know' where 0 degrees is in relation to the incoming beam?
For clarification I am not talking about the angular dependent interference due to Rayleigh or Mie scattering. I hope this makes sense.

 A: It is momentum that defines the incoming direction and momentum transfer the outgoing one.
The photons, quantum mechanically carry momentum equal to p=h*nu/c . Momentum is a vector and defines directions.
An electromagnetic field is an emergent classical quantity built up by innumerable photons.
There exists also a momentum defined for the classical field where the Poynting vector defines the direction, if one ignores the quantum dimensions, but you are talking of electrons which are  quantum mechanical elementary particles.
A: Let me offer you a slightly modified version of your question to illustrate a way of re-formulating it your thought process.

How does a pool ball know from which direction the cue ball hit it?

The answer is the same in the sense that "the particle" does not know all by itself, "the system"1 has certain invariant quantities (like momentum and energy) and some of those are vectors and have directions built in. Just like the cue ball, the incident light carries energy, momentum and angular momentum and those conserved quantities must be respected by final state of the system.
This approach is, perhaps, more natural if you use a quantized (i.e. photons) picture of light but it still applies with a classical view in which the energy and momentum input is continuous.

1 That is the "the particle" and the incident light or the combination of the two pool bals.
A: This is just a complement to the previous answers which give the correct response. If you want to think about it in an intuitive way, imagine that the interaction between electrons and photons becomes weaker. In the limit when it becomes nearly zero, the light will be almost not scattered at all and will continue in a straight path.  
A: Mie scattering and Raleigh scattering are classical effects. It should not be necessary to talk about photons in any answer.
The directionality of scattering in both cases is determined by the polarisation of the incoming electric field vectors.
In both cases the light can either be polarised in a plane perpendicular to the direction of the incoming transverse electromagnetic wave. This defines two directions in space - the direction of the electric field vector and the wave vector of the electromagnetic wave.
For unpolarised light, the electric field vector is still in the plane perpendicular to the wave vector, so there is still one defined direction associated with the incoming radiation, which is perpendicular to the plane of the electric field.
For Rayleigh scattering, the scattering of linearly polarised light is directional in the sense that it has the classical dipole radiation pattern with no radiation emitted along the axis of oscillation, which is the polarisation direction of the incoming wave. For unpolarised light there is no preferred direction of scattering and the scattering particle doesn't care from which direction the wave is coming.
For Mie scattering there is directionality irrespective of whether the incoming light is polarised or not. The directionality is imposed by the boundary conditions of the problem in the same way that Snell's law for transmitted light through an interface is defined by the angle between the normal to the surface (of a particle in this case) and the incident electromagnetic wave direction. The direction of the incident electromagnetic wave is in turn perpendicular to the plane of the electric field.
At a deeper level, I'm sure it is true that the direction of the momentum vector of the consituent photons, which is coincident with the electromagnetic wave direction and with the Poynting vector of the electromagnetic field sets a fundamental axis and direction for the problem, but the concepts of the photon or indeed the Poynting vector are not needed to predict the scattering properties.
