As much I'd want to continue the OC in a sequel, it's a cold hard truth that full-fledged rpg sequels don't let you start out with bad-ass high level toons. So, DA2 would likely work a lot like Kotor2, and put the new PC at a distance from all the cool old characters. By the way, Bioware, I hated that kotor did that, especially since it had such a horrible, cliffhanging non-ending.
And, despite what I said, I would love to be able to continue playing with all the old characters (or the principal ones at least). So take this as fodder for an expansion if not a full-fledged sequel.
I think after four blights, and four arch-demons, major players in Ferelden should begin to question the wisdom of sitting around, waiting for darkspawn to unleash the remaining old gods and wreak more havoc across the continent. Not only is the toll in elf/dwarf/human lives immense, but defeating a blight hinges upon having Grey Wardens, which were nearly wiped out this last time. Correct me if I'm wrong, but I don't think there's any certainty that another blight could not occur soon, perhaps before Ferelden and the Grey Wardens have fully recovered.
Here's the set-up I envision: Orzammar's king (whether Bhelen or Harrowmont), uses the recent aliance against the blight as a springboard for proposing a search for the remaining old gods. With the carnage of the blight fresh in everyone's minds, the proposal to destroy or neutralize the old gods before the darkspawn get them would seem very wise. However, profound disagreements would immediately emerge over what to do if the old gods were actually found. Orzammar's King, the Chantry, and the human king (whether Alistair or Loghain) would favor destroying them. The Dalish elves and the Circle of Magi would favor studying them for various reasons. Fearful of putting the cart before the horse, all factions agree to set this dispute aside and focus on actually finding the old gods first. The Circle of Magi and the Chantry then reveal ancient research that suggests that the archdemon's destruction was not absolute-- some remnant of its consciousness likely lingers in the Fade, and this remnant may have clues as to where the other old gods are. The game begins with the Chantry tentatively helping the Circle seek the archdemon within the Fade, and the Grey Wardens being chosen to find the old gods, since there will presumably be a lot of darkspawn in the way.
This premise can adapt to any ending. If the PC (or someone else) agreed to Morrigan's ritual, the Chantry and the Circle point the Grey Wardens toward her and her child's location. That the PC would agree to her ritual, as risky as it was, severely damages the PC's standing with the Chantry, setting in motion later conflict. If the PC or someone else died to "permanently" defeat the archdemon, then the player's game would begin in the Fade itself, with the sacrificed Grey Warden's consciousness locked in struggle with the archdemon's.
If the player's game starts in the Fade, it would make sense to be contacted and assisted by Morrigan, who, since the Archdemon's death, has learned as much as the Chantry and Circle have. She resolves to resurrect the Grey Warden, using the bond between the Warden and the archdemon to draw enough magical energy to perform the otherwise impossible task. From either beginning (tweaked depending on who performed the sacrifice or ritual), all roads run through Morrigan. Having either the old god child or unique insight into the resurrected Warden's connection to the archdemon, she would be the initial guide to the first old god. It would be logical, then, that if the player slays the old god outright, Morrigan abandons you and you have to find the rest without her assistance. From there it's just crazy epic adventure goodness.
Obviously, for this to work, a lot of the OC's plot twists have to be addressed or molded into a single narrative within the sequel/expansion (for instance, the differences between Bhelen and Harrowmont's dialogue here wouldn't be that different, both would want the same thing regarding old gods). If I was forced to choose canon, I would opt for:
Alistair and Anora rule jointly with Loghain executed, Harrowmont rules Orzammar without the Anvil (makes him more desperate for help), Circle saved, Elves saved with Zathrien dead, Arl Eamon and entire family still alive, Urn of Sacred Ashes in the Chantry's possession (which emboldens them for an anti-old god campaign).
Whether the PC is dead or not would be save game dependent, since Morrigan resurrects him/her. If PC is male and agreed to ritual, PC performed it personally; if female, Alistair did.
Oh, and most bird species in Ferelden are now extinct, all of them mysteriously crushed flat...
This would make an awesome straight-out sequel, but would be nice as an expansion too.