I actually make from scratch cake with sour cream all the time.
In my experience, just replace the liquid (whether it be water or milk) from the box mix instructions with sour cream. It will result in a thick batter that is delicious. Of course, you still need to add the butter or oil that the recipe calls for.
I don't know about pudding mix. If I remember, you can just pour the box mix in. ?
Hope this helps,