I'll start out by saying that when I hear the words "strong female character" the term "ball buster" comes to mind. I don't care for female characters with a chip on their shoulder that they then blame on every man in existence. That's a turn-off to me. If a female character is rude to a guy simply because he's a guy and she has that "you know how men are" mentality (while rolling her eyes), that's a turn-off to me.
But, I tend to be a trusting person. I won't think badly of someone until they prove me otherwise, and generally, they have to prove they're a bad person over and over before I'll "get it" and back away from them. Admittedly, I tend to trust men more than I should, and have a difficult time trusting women, understanding them (even though I am one).
Anyway, I'm not sure what my personal definition of a strong female character would be. I have a female character who I believe is very strong. She could maim and torture her man with her supernatural ability, but she chooses not to. Her romantic interest is thrown into a relationship with her (what he refers to as "an arranged marriage" simply because, due to his own supernatural problems, she's the only woman he can be with) and he's still pining after his dead wife. She could influence his mind in such a way that he'd forget he ever had that first wife, that he'd think he was in love with my female MC, but again, she chooses not to influence him for her gain. In my opinion, that's damn strong. To see what you want and know you could have it just like that, but you deny yourself. He even asks her at one point why she doesn't just "make" him love her and she says she wants his love for her to be real, not manufactured.
Go ahead. Throw your own definitions in there. I'd love to hear them!