Okay, let's start with the realization that HPL was pretty inconsistent when it came to naming his monstrous civilizations. He uses the term Elder Things for the polyps from SooT as well as for the Old Ones from AtMoM.
As far as I know, it's like this:
AtMoM Elder Things = AtMoM Old Ones = SooT Old Ones = what we call the Elder Things.
SooT Elder Things = what we call flying polyps (where did that name come from, anyway?)
AtMoM Elder Things /= SooT Elder Things
I can find no reference to the war between Polyps and Elder Things (I know in the Shadow Out Of Time that the Polyps kicked the Yiths butts eventually)
Shadow Out Of Time was written three years after Mountains Of Madness, so the polyps can't be in the AtMoM description of the Elder Things' history. I couldn't find any reference to polyps (or Elder Things) warring against Old Ones in SooT. I'm not aware of any other HPL source that mentions that history, so I guess there was no war between them.
Also, when did the Elder Things war against the Yiths?
I'm not sure. If you mean the AtMoM creatures, there is no date or time stated in the story, though there is a reference to the Great Race battling Old Ones.
If you mean the polyps, the Great Race fled before the war could really start, if I remember correctly.
The Elder Things are known to have warred against the star-spawn of Cthulhu, the Great Race of Yith, and the Mi-go
Elder Things meaning the AtMoM Old Ones? Yes, that's correct. The first and third are supported by AtMoM, the second is supported by SooT.
When they attempted to colonize the oceans, the polyps were driven back by the Elder Things. Thereafter, they restricted their habitats to the surface world.
I can't find any evidence for that. And the wikipedia article doesn't give a source for that.
I hope I could clear this up a little. If I made any errors, please correct me - it's been a while since I've read SooT.