I'm more interested in technology-agnostic solution which accurately resembles underlying particles. E.g. how would one approach this problem from math/physics standpoint?
The issue with the math/physics solution is that given the sheer scale of astronomical quantities it is wholly impractical to go the "fully accurate" route.
The reason that a nebula appears to be a solid glowing thing isn't that there are a bunch of stars and gasses very close together; it's that each individual glowing star and piece of gas is far enough away from us that we cannot resolve the individual pieces -- given their distance from us, they are so close together that the angle between adjacent points is small enough such that our eyes can literally not differentiate between different stars or heated gasses in the nebula (Look up the Rayleigh criterion if interested).
Furthermore, the propagation of light from a nebula, or more accurately from anything, follows what is known as the "inverse-square law:" the intensity of the light changes in inverse proportion to the square of the distance from the source. So, doubling the distance between you and a light source would quarter the intensity of light hitting you. Perhaps slightly less important for a computer game, but the result is that brighter parts of the nebula may not end up looking that much brighter than other parts (but of course, it depends on the actual brightness values involved).
And the actual frequencies of light which we can see are a product of black-body radiation. In simple words, the wavelengths of light emitted by a light source depend upon the temperature of said light source. And to make things even more complicated, the dopper effect, which applies to sound, light and other electromagnetic radiation, specifies that any relative movement between us and the observed light source can shift the frequency/color of light we observe towards either red (moving apart) or blue (moving closer), phenomenons called "redshift" and "blueshift" (Scientists are so creative at naming things!)
And that's not even getting into the formation & structure of your galaxy or nebula in the first place!
Replicating such accurate behavior in a computer program would be a rather daunting effort: the creation and simulation of many, many individual particles (stars), with a distribution of distances and temperatures, and then determine accordingly how a layer of gas around the stars would be heated and which frequencies of light it would emit at various spots. And that's all before you can even attempt to figure out how to draw it.
If you want to go that route, good luck. If at all possible I'd recommend doing the calculations and rendering offline and then just use a selection of pre-made images for your final game.
Still reading? Don't want to try to do this completely from a math/physics viewpoint? I don't blame you.
Anyways, my suggestion for how to do this in a somewhat reasonable way without too much pain:
Start off by assigning each of your star-particles a color and brightness (probably via some distribution function)
Add a bit of glow around each point according to its brightness and color. Individual stars would probably still be somewhat visible at this point, but the space between stars shouldn't be too much darker.
- If you want more uniformity of light, take the entire thing and blur it a bit more so that it, on average, looks about the same brightness. Ideally there would still be some bright spots, but not too many.
Optional -- Overlay some darker "clouds" to simulate masses of gas obscuring or blocking the light behind.
Essentially, take your point-lights and blur them together until it looks okay. It might not be perfect, but if done properly I don't think it would look too bad. (I'd try to make an example picture for you, but I'm not great at Photoshop)