I seem to recall in one of the first scenes of Episode IV Leia says something to the effect that her father is a powerful man and will be outraged that Darth Vader has kidnapper her. I suppose she means her step-father, since she is talking to her real father. Does anyone else recall that?
Yep, I do. She probably figures that her "father" is her real father. She wasn't told that she was adopted.
Yes. I recall that. I always assumed that to mean her adopted father. It would make sense. Keep in mind that Leia didn't really "know" she was Luke's sister or that Vader was their father until near the end of Return of the Jedi, even though she said "somehow I've always known." At one level I'm sure she did, but not consciously, I don't think.