But the House of Mogh was completely taboo ever since Worf's father was blamed for - whatever it was he supposedly did. Or am I remembering that incorrectly?
The impression I always got was that a Klingon house consists of: a) immediate/extended family and b) loyal retainers. As far as I remember, Kurn is supposed to be the only family Worf has left in the Empire.
And if the House officially didn't exist all that time, wouldn't the loyal retainers have gone off to join some other House whose honour was actually intact?
I suppose I don't quite understand how the Klingon House system is supposed to work. Another confusing case is the House of Martok: Worf describes it as having a highly honorable reputation, Martok's wife is even supposedly descended from an ancient Klingon princess, yet Martok himself is supposed to be a 'common soldier from the Ketha lowlands' with no noble blood. (I think that was the phrasing used)
The House of Mogh became taboo in 2366 and remained so until 2367. It became taboo again in 2372. Kurn was memory wiped and join Noggra's Worf later joined the House of Martok. So at that point the House of Mogh ceased to exist.
Memory Alpha wrote:
The Great House
also included various properties and holdings, and commanded military forces. The rulers of the twenty-four most powerful Great Houses formed the Klingon High Council.
From that, I would say that the folks living on the land and serving in their forces are members of the House, though not blood relatives of the House's leader.
Great Houses which were gravely dishonored by the actions of their rulers could be disbanded, and their holdings claimed by other Houses.
And from this I would say the other houses claimed the former holdings of House Mogh.
Martok is a special case. He was elevated to royalty based on his military skills and victory. It's happened on Earth too.