I just figured that their 'nephalem' powers were awakened, in a similar way that Uldyssian's powers were. Except, Uldyssian called himself an Edyrem, but he is essencially the same thing as the Nephalem, just a different generation. I suppose it is the generation that makes all the difference... but still, its close enough. Its much easier for the Ancients to just call themselves Nephalem rather than try and explain that they are technically nephalem but not quite because they aren't the first generation, but they still have the same powers.
Oh yeah, and Nihlathak is just an Elder Barbarian. The Elders have spells and rituals that regular Barbarians do not. But he's not a Necromancer, he just somehow gained demonic spells. He seems to have made a deal with Baal fairly early on, because he was the only one that wasn't killed by Baal's minions when all the other Elders were. I'd say his deal gave him extra powers.
All of the Elders, save Nihlathak, sacrificed themselves to place a protective ward around Harrogath.
Quote from LoD Manual »
7th day of Montaht, Matins It seems that I am not the only one who cannot sleep. Qual-Kehk readies his men even now, as I ready myself. This morning, I shall propose that we perform one of the long-forbidden Druidic spells of warding. As Elders, we alone are capable of summoning such tremendous energies. Though the ward may drain us of vital magical reserves, if our land is to be saved we will do what we must.
Our people once considered the Druids brethren - but after the terrible Mage Wars, the druids were exiled to the harsh wilds beyond our homeland. Since then, our Elders have kept their fearsome Druidic powers a closely guarded secret.
The danger of unleashing such powers once again terrifies me. If done incorrectly, the warding spell could consume us all well before the arrival of Baal's army. However, I have studied the rites, and I am confident that I can cast the warding correctly with the Council's help. The ward will bar passage to any spawn of Hell - even Baal himself. I intend to place it around the entirety of Harrogath.
Casting the spell in this fashion requires that all seven Elders venture outside the protective walls of our city. The danger is great...We may all be killed. However, I see no alternative. I go now to take this matter before the assembled Council of Elders.
Actually, listening back to their speeches, the Nephalem in the game seem to fit in exactly with The Sin War Trilogy.
Quote from Anya »
"Many outsiders believe that the fantastic stories about our ancestors, the Ancients, are but fables. However, I believe that the Ancients were more than human -- that mankind has fallen from what it once was."
Quote from "QualKehk" »
"The Ancients are not our enemies. Remember that! They are our ancestors -- our gods."
Quote from The Ancients »
"We are the spirits of the Nephalem, the Ancient Ones. We have been chosen to guard sacred Mount Arreat, wherein the Worldstone rests. Few are worthy to stand in its presence; fewer still can comprehend its true purpose.