I am near-sighted. Here is the phenomenon: I stand in front of a light source that is situated on the ceiling so that it reflects off my eyeglass lenses and appears circular. It is a white light source but appears shifted a blue-green in the reflection. When I tilt my head so the reflection is in the very corner of the lens, the circle becomes dramatically oval-shaped and the color has shifted. On the side closest the edge it is red and on the more medial side, blue. First, why is the reflected image (no head tilt) green? Second, why does the image shift in color when situated on the edges? I am guessing the thickness of the lens has a role to play, being thicker on the edges but I don't know how to explain all of it. I'm am guessing also as I tilt my head the angle may hit a critical point where it acts like a prism where you can get all the colors out. Again just speculating here though
Probably the colors are due to an antireflection coating or UV rejection coating on your lenses. Those shift color with the angle of reflection.
You are right that the oval shape of the reflected image of a circle is due to curvature of the lens. If you look at the reflections in, e.g., a christmas tree ball or fishbowl, you wiĺl see a similar effect ( though not the color shift). To see a similar color shift, you could look at reflections in good quality camera lenses or binocular lenses.
It might even be due to spherochromatism, coupled with barrel distortion?
White light is polychromatic in nature. Spherochromatism (also called chromatic aberration) is a phenomenon where light rays of different wavelengths (as seen in the composition of white light) are deviated to different angles within the lens, such that they all do not converge at the same focus. This causes "coloured fringes" to manifest at the edges of images. It's mainly because of an irregular curvature or refractive index in the bulk of the lens. This might be why your images have blue or green on the edges.
And the reason the fringe colours change while you move your head must most likely be because of your eye's accomodation. As you look at things of different distances from your eye, to focus that light and view objects clearly, the human eye changes the focal length of its lens which is termed accomodation of far and close objects. By changing this focal length, out of the various colours refracted, only one colour must be reaching your retina at a time, most likely causing the colours to change as you move your head.
"Barrel distortion" most likely is the reason for the ovoid shape which you talked about. This is also called a fishbowl effect, and is extremely common in the concave lenses used to treat myopia; which you must be using, since you mentioned that you are near-sighted. Its because of a changing curvature of these concave lenses at the edges by which image magnification decreases at their peripheries, causing an enlarged image in the centre with lesser-magnified images at the fringes giving an ovoid, fishbowl effect. The opposite is observed in convex lenses, where the peripheries are magnified more than the central regions, causing "pincushion distortion", as shown in the figures I've attached below.