Do gravitational waves affect light? Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect, and shouldn't this effect be present wherever there's gravity, for example shouldn't there be a "shimmering effect" when observing distant stars/galaxies as their emitted light is "bend" this way and that (like heatwave-shimmer)?
 A: The truth of the matter is that we don't know.  Gravitons are a theory slowly becoming accepted but there is simply little evidence to support them as a viable theory on how gravity works.  Gravity is still just the magical notion that was devised centuries ago.  We only know that gravity is not constant and it is the only force not conforming to the theory of relativity.  We know this because the path and direction of distant galaxies in our expanding universe are not moving in directions that our gravitational math expects.  Something is wrong there.
What some of us are confident of is that light particles are physical things, and like all physical things they adhere to the laws of gravity.  Just as our bodies do.  
I think your question is why isn't light reaching us from distant stars shimmering, as might happen when someone holding a flashlight pointed at you moves it from right to left or up and down across your vision.  Even if the star were moving from left to right or up and down (which it isn't) it would still not shimmer - because it's light is emanating at all angles, not a steady stream like a focused flashlight.  And although light from stars are bent by the gravity of other solar systems, planets, and even other galaxies, it stays bent.  It doesn't bounce back to it's original path like a spring.  Therefore when it gets to you it is a steady stream on a fairly straight path from it's last bending point.  
The most interesting thing about your question is that light particles are also affected by the gravity of our Sun and Earth as well.  Which means the star's light particles are most likely on a slight bend as they reach our eyes as we stand on this huge gravitational ball called Earth.  I personally believe that planets attract light particles, as well as neutrinos, electro-magnetically.  But that is not a popular theory.
I think you might be interested in learning how our eyes work, the retinas being struck by gazillions of light particles from different bending angles constantly.  Everything we see is due to photons bouncing off of objects and then into our eyes, which have rods and cones that convert them to neural vision.  Although the particles could have bounced 100 times or more off of things before reaching our eyes, they are on a direct and straight path from the last object they bounced off of, giving us that object's distinct color.  It gets a little more complicated than that with the notion of light particles emanating in waves, but it's all relevant.  
A: Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect
I conceive the question as one referring to General Relativity (GR) which is an entirely classical theory, and not to a (thus far missing) theory of Quantum Gravity.
The point of view of General Relativity is that free falling reference frames are true inertial frames (ie where Newton's first law holds). Thus, viewed from within a free falling frame, light goes on a straight line:  a person inside a free falling elevator, will see a straight light ray. Then, another person, standing on firm ground on the outside the free falling elevator, will thus see a bend line.  
From the above, it is clear that everything that has a gravitational field will bend light rays.  Masses clearly come with a gravitational field.  And because of the equivalence of mass and energy, $E=m c^2$, everything that has energy, has a gravitational field, too.  
However, the energy density of a gravitational wave is tiny. So the bending effect will be tiny.
Nevertheless, the "shimmering" you refer to can be observed if the gravitational waves are humungous: this is just what LIGO did with gravitational waves stemming from the merger of black holes.
A: 
Gravity "bends" light, predicted with theory of relativity and subsequently observed: how does gravity and gravitational waves achieve this effect,

Physicists are hopeful that gravity will be quantized similar to the other three forces, and that gravitational waves are a confluence of gravitons. There exists the classical general relativity where the photons/light are following the distortion of the stress energy tensor due to a gravitational source of a star, the geodesic, and bend.  In a quantum mechanical view, the photons interact with virtual gravitons and change directions into bending.

and shouldn't this effect be present wherever there's gravity,

wherever there is gravity, in the QM framework there will be a photon graviton interaction, but it will be higher order and the gravitational constant is very very small, 

for example shouldn't there be a "shimmering effect" when observing distant stars/galaxies as their emitted light is "bend" this way and that (like heatwave-shimmer)?

The photon/light bends when passing very close to  gravitational wells, but  the probability of changing directions randomly ( shimmering) is very very small, not detectable because of the gravitational constant.
The LIGO experiment has enormous spatial accuracy , so it can detect small distortions of space from a passing gravitational wave, which affect the laser light of the experiment. These conditions are not held for general star light . The LIGO experiments gravitational wave is built up by  real gravitons, building up the gravitational wave (of course assuming quantization of gravity analogous to the other three forces). The interactions of light in bending around stars is effected by the exchange of virtual gravitons, the gravitational field. LIGO is a gravitational wave detector.
