"They say King Helseth has made an alliance with House Dres and together they've picked apart the ruins of House Indoril"

"I hear House Indoril is in ruins, and House Redoran is besieged by Nords from Skyrim" <--Not exact quote but same topic

So I've played TES III IV and V a few times now and find I'm still missing things. I thought House Indoril was the house lead by Indoril Nerevar and was destroyed [Like house Dagoth] so why would people be talking like it was recently destroyed? Or was House Indoril still around during Morrowind [Perhaps as the Temple's House?]

Also is it ever explained why the Nords are attacking House Redoran? I admit I never did the House Redoran quests in Morrowind [Hlaalu ftw]

House Indoril exists during TES 3, yes. It's the house to which the Ordinators largely belong, and while Indoril has close ties to the Temple, they are distinct from it during the Third Era (the Dragonborn expansion to Skyrim explains a bit about the fate of Indoril after the Red Year). House Mora is a lost house, a minor one, to which Nerevar belonged before he married into Indoril; this might be the one you are thinking of.

I assume the Nords are attacking Redoran because the borders of Morrowind are under dispute. The Redoran district of Morrowind is the westernmost, in the Velothis, and has at times during history been subject to war with the Nords or even occupation.

My two cents:

By time of Morrowind, House Indoril was already pretty entwined with Tribunal Temple, enough for casual observer to draw conclusion that Indoril == Temple, but still a measure of being separate entities.

Being as entwined with the Temple as they were, ALMSIVI fall weakens their position even further, to where Helseth and Dres can capitalise. Now, in 4E Morrowind, Indoril and Reclamations temple are indistinguishable.

Ah, here's the quote from http://uesp.net/wiki/Lore:On_Morrowind that describes Indoril's decline after the armistice:

Hence the retreat into the Temple, and why it is described as "in ruins".