Ellipses, I read your post earlier and have been thinking about it all day. Not sure that I have anything of value to contribute, but it just really brought me back to my own struggles at that age. I always felt like an outsider for a variety of reasons, in addition to my own giftedness, I never fully fit into a single social category or group. I think it is great that you are trying to help your daughter through this AND that she is comfortable enough to share her feelings with you. I hid my own feelings of loneliness from my parents.
My own children are much younger than yours, so I don't know what it is like to parent a child through this, but here are a few things that I have thought about regarding my own experiences, maybe they would help.
--I read some research recently that said that kids feel like they need to have alot of friends, but in fact, 1 or 2 really good friends are really what helps teens through this, mental health wise. This was definitely true for me, I developed one very close friendship and a couple more fairly close friends and that really made a world of difference. So maybe you could help your daughter foster one or two close friendships rather than focusing on the being part of a larger group or crowd. Maybe someone in one of the activities she participates in? Chances are there is someone else feeling like an outsider too who might welcome a new friendship. If she were younger I would say, call the parent up and set up a playdate if she's too shy to do so herself, but I don't know what would be appropriate intervention at 14. But maybe you could find some way to encourage a new friendship though.
--I remember when I was a junior in high school an adult said to me, "Enjoy high school, it is the best time of your life!" and even at 17 I remember pitying this person. If HS is the best time of your life, that is just sad. HS was NOT the best time of my life (and I would imagine it isn't for alot of people). Things do get better! And, in light of my recent 20 year HS reunion, IMO those who seem to be on top in hs are not necessarily the ones who seem to be the most successful, happiest, etc. later in life.
--I think a pp mentioned something like this, but if the therapist doesn't help, perhaps an adult mentor would. Someone who is happy and successful now, but also struggled in HS?
Don't know if any of this is helpful to you, but I just wanted to say, I remember that feeling and it CAN be survived. Big hugs to your dd!
