There's a possibility that's often overlooked - perhaps the Deep Ones are demigods or entities which don't fall into any of the traditional pantheons of the ES Universe. If we look back to Arena and proto-Arena lore, there were many many unexplained deities and champions in Tamriel which were not directly associated with the Divines or the Daedra. It might be that the Deep Ones simply represent some forgotten pagan entities from the infancy of Tamriel, who were perhaps in place before the Earth Bones finished falling into place. Or maybe they ARE Earth Bones - lesser ones who never made it into any official pantheon. Or perhaps the Hackdirt citizens are crazy.
That's the best explanation I've read beyond it being an Easter-egg tribute to Lovecraft.
For what it's worth, the Deep Ones from Lovecraftian lore followed a deity known as Dagon, whom in turn served the Old God, Cthulu. (Or was another aspect of Cthulu. I'm not sure) No equivalent of Cthulu exists in TES lore that I am aware of, but the being Dagon is a Daedric Prince who happens to be the main nemesis behind the main quest. So perhaps this is simply an extension of the Mythic Dawn or another cult of Dagon, and maybe the Deep Ones are Daedra. This would explain why they were gone for a long while, but recently returned when the Oblivion Crisis began.
Mehrunes Dagon doesn't line up nicely with real-world Dagons (Lovecraft's Dagon or the Dagon of the ancient Middle East). Lovecraft's Dagon is a tentacled sea monster, and the ancient Dagon is a god of agriculture. Latter-day depictions of Dagon and (probably specious) reinventions of mostly-lost legends make Dagon out to be a fish-god, which is a tradition Lovecraft drew on. None of these have a Dagon who is a god of fire and destruction and carries a damned big axe.