I can't get Sims 3 to work on Origin no matter what I do. If I purchase the game on Steam, will I be able to use the expansions/stuff packs I have on Origin?

The short answer is no. You would have to repurchase all of the EP/SPs on the Steam platform. I did this myself a couple of years ago just to get away from the Origin/1.69 structure because while it mostly worked, it was incredibly annoying and not stable. During one of Steam's deep discount 70-80% off sales, they run similar ones a few times each year, the entire thing except for Katy Perry which Steam does not carry anyway cost me less than $100 (USD).

There is supposed to be a Registry trick way to get Origin purchased EP/SPs recognized by Steam, but it doesn't work for everyone and of course it is not officially supported.

I take it that EA's Answers HQ board was no help in getting Origin to work on your end?



That's the wrong way around, I'm afraid. The OP does not wish to run their Steam purchased games on Origin because they cannot get Origin to run the game at all. They wish to run their Origin purchased games on Steam with no Origin involvement. It doesn't work in both directions.