*late*
*haven't gone through the entirety of thread so apologies*
This is creepy. Can anyone shed more light on what the Calling is, other than it being a song of doom? I'm inclined to believe that the Old Gods were dragons with a piece of the Elven Gods soul in them and that someone manipulated the magisters into entering the Fade. I had an idea that red lyrium is somehow made from the blood of ancient dragons through blood magic or similar since (I think) it seems to predate the Blight? I think the Blight was a mistake since Flemeth/Mythal doesn't like it very much. Also, I think she waited until now because she needed the essence of whichever Elven God that was in Urthemiel in order to open a locked Eluvian.
It's a mixture of what other people have said.
The Old Gods have a song they emit from beneath Thedas. It's referred to as the Old Gods' Calling, the Song, what-have you. All valid names for the same thing. The darkspawn hear this song as something perfect, and are drawn to it. They spend most of their non-Blight time digging for their prisons. But the moment they reach out to touch the Old God's perfect form, it is corrupted, and rises as an Archdemon. It leads the darkspawn in a massive invasion, leading to horrific levels of death for everyone. Irony sucks.
Wardens, having taken the Taint into themselves, also hear the Calling if they get close enough to an Old God, or something similar when close to Corypheus. (I may be wrong on that last point.) At a certain point, it varies depending on whether there's a Blight or not, exposure to darkspawn, natural fortitude, and just plain RNG, the Taint accelerates. They begin to hear the Calling of the Old Gods full blast, and the Taint begins to twist them into specialized ghouls. When they start getting twitchy, they follow the tradition of the Calling and go to the Deep Roads to meet their death slaying darkspawn. If you want to know more about the Calling, in the Old God and the Grey Warden sense, I suggest you read The Calling by David Gaider, which has all the Blight goodness you'll ever want. 
I'm in agreement with you about the elven god essences being in the Old Gods.
Flemeth probably uses the Dark Ritual to cleanse her former Pantheon members of the Blight.
There's a theory going on in the Solas thread that lyrium is the blood of the Forgotten Ones, who are also the dwarf gods worshiped during the time of the Primeval Thaig. (The Titans mentioned by Kieran.) And it seems Andruil was exposed to the Blight and brought it back to Thedas, infecting Elvhen. Something contained it, and contained the Primeval Thaig, for a time. But eventually the Vints busted open the Black City and became carriers.
I figure you probably already know most of the Blight stuff, but I figured if anyone else has only ever played Inquisition they might want an info-dump. 