Oh, I thought the line was perfect! I mean, you have to understand that the books were written over 50 years ago, and writing/speaking styles have changed significantly. It just would seem over-dramatic for Eowyn to speak the way she did in the book. And we all knew she was going to say some powerful, feminist reply to the Witch King's comment, but it still brought excitement because it wasn't like the cliche that was expected. Miranda Otto had an amazing performance in that scene--just incredible.
I was a little confused about the Ringwraith's deaths too, but there's no need to really think about it too much--all the evil creatures died after the destruction of the One Ring.