Dragon Age: Origins and the Ultimate Edition

Nope. They even count as separate entries on Steam.

As far as I'm aware, the only way to get the DLCs on Steam is getting the Ultimate edition.
Your Steam copy should entitle you to an Origin key, though, and on Origin you can still buy the Awakening expansion.
The other DLCs can only be bought with the obnoxiously expensive Bioware points, regardless of platform.

I had this issue with Steam as well. The work around is this:
Once you have the game installed, make sure it is linked to your origin account.
Once linked it will show up in your Origin account and you can use certain giveaway keys/promotions to get some of the DLC.
The rest of the DLC, you can purchase with cash or if you play enough origin games, you can earn the points to get the DLC.
If you run Raptr, (AMD's Gaming console/platform/store app), you can also get a few more DLC packs - or you used to be able to at any rate - depends what they have on the rewards list at the time.
I think in total it cost me AU$10 to get all the DLC after using all my points/coins/free keys.

Some of the DLCs are pointless, some are nice. But I guarantee you even if you play just the base game, you'll have a great time. Here's some info on the addons, so you can decide if it's worth it:
The Stone Prisoner has a short quest and gives you a companion.
Warden's Keep also has a storyline and gives you a chest to store items and two skills (optional).
Return to Ostagar shows you what happened after the first battle and gives you a second chance to get one of the companions.
I cant exactly remember, Golems of Amgarrak.
Witch Hunt is the last of all and is the end of the game.
Feastday Gifts and Pranks is pointless. It gives you some more interaction with your party in camp - nothing more.
Leliana's Song and Darkspawn Chronicles are also almost pointless. The first is a background story for one of the companions and the second is the final battle trough the perspective of a darkspawn.
Edit:
Oh, I've forgot Awakening! It's the only big addon. It has some of everything - big storyline, companions, skills, a base you can upgrade and a big decision at the end.

you can trade for Awakenings. I can get it for two keys; with some legwork, maybe less

Please note, it'll cost you at least three times the cost of Ultimate Edition alone, to obtain all the DLCs separately [through Origin/Bioware points].
Of course, the higher base pricing ($71 vs $30) is bad enough- but, additionally, Bioware point DLCs/Awakening basically never go on sale (I believe they've gone 20% off before, while DA:Ultimate has gone as low as $5, a couple of times).

In other words, even if you own the base game- If you plan on playing with DLCs, just forget you own the base game. Like a Bethesda or Paradox or Gearbox game, it's time to throw in the towel and accept you have to completely rebuy the game.

Flip side, if you're the type that doesn't worry about "playing the perfect version of a game", then the base game is fully-functional, rich RPG experience.

So really, it boils down to what your preferences are.
But really- if you're going for Ultimate, wait patiently for a sale. Bioware points will bleed you dry.

get the ultimate edition, you can delete the old licence for DA:O from your library if you don't want duplicated games.