Does anyone know...

Aside from the biographies, was there ever any sort of formal storyline behind dota? Like who the dire are and why they are after the ancients, etc... ?

From what i recall from DotA 1 there wasn't any such story, though there are stories of heroes who cross path such as brood mother, nyx assassin and.... I can't exactly recall the last one but i think it may be weaver. Broodmother was having an affair with weaver or nyx assassin if i recall correctly. I remember my cousin was reading the stories behind each individual hero when he had free time since he had no internet and couldn't really afford a decent gaming computer.

"Before the world was even created, there was an unending war between two entities, much to the chagrin of the vast Primordials; and thus they were locked up together inside a prison: the Mad Moon. As the world of Dota 2 captured the Mad Moon inside it's gravitational fields, all seemed fine, but underneath the crust, the two inhabitants were at work on freeing themselves. After what can only be thought of as a long time, they managed to free themselves and fell together with some of the remains of their prison to the planet. But nothing really is that simple, as some of the entities on the battlefield clearly seem to have had a hand in this. But, however cloudy, the visuals to this backstory can be found here.
What fell to the surface would influence the civilizations that settled around these fragments, granting them kinetic energy, mana, protection, even resurrection. However, the entities could not let go off their pasts and soon, they were at war again, this time using not only the civilizations, but even calling forth heroes to fight their little quarrel."

Summary found from this awesome lore thread : Dota 2 Lore Megathread

Go read it, its pretty interesting.

If you played the tutorial, you gained pages into the Archonicus.Read that.