There are several issues with Strange Girl's description (and definition). It states that the trait that examples share is they are protagonists but most of examples are not. The description is pretty vague and broad as well: It's unclear how "strange" a character is supposed to be in order to be counted as an example. It also says that a character can be of any personality (The Messiah and Straight Man characters are included) as long as they stand out from the "series norm" but in several examples the Strange Girl isn't the only unsusual one.
My experience with the Strange Girl hasn't always been protagonists. The unifying trait seems to be that this character stands out as they aren't particularly grounded in reality or social norms.
I think it's supposed to describe people like Luna Lovegood and Pippi Longstocking, but ultimately, it may be too vague and broad to be useful.
I thought this trope needed attention since I first came across it. It is used for all sorts of characters whose only common points is being a young woman, a Foil of some sort to the protagonist and with some pervasise oddity of thought or behaviour. It seems to cover those who do not fall under Manic Pixie Dream Girl. I cannot see any trope.
It seems to me that someone took a phrase in common use for certain characters and made an article out of it without thinking to delineate a trope. Unless someone comes up with a meaningful difference from our other strangeness tropes and why it should be gender-defined, I say we cut it.
I took a look at its wicks. Insofar as there's a pattern, it does indeed seem to be a milder, less directed version of Manic Pixie Dream Girl. A foil to the male protagonist who is slightly mysterious and with impenetrable thoughts, crazy in an innocent, harmless and endearing way, either a love interest or a close ally.
There's something of a trope here, but there are also plenty of wicks that do not fit and I can't tell what they're aiming for. It doesn't help that so many are zero-context.
I think this one needs rebuilding from the ground up.
I don't think this should be cut (without redirecting it somewhere at least), I still think it's a trope although it may need heavy revising to be useful and less vague.
Anyway, is there any reason why this is gender-specific?
I don't see how this is a trope. "Character who is different from the characters around her" is way too vague. In many genres it is pretty much a given that the protagonist is different from the supporting characters - that's why the protagonist gets the plot resolved and the supporting cast doesn't. The list of examples is basically an arbitrary list of characters that some troper find unusual. There's very little that Susan Sto Helit has in common with Luna Lovegood, for example, or that River Tam has in common with Willow Rosenberg.
I think we should cut this.
Willow is just the smart, socially awkward character. I don't know Susan Sto Helit. The page description says, "Usually she is in touch with the supernatural aspects of her setting, even if she doesn't have powers herself." Luna talks about things that other don't believe in and River is super smart and crazy. She tells one character that she can kill him with her mind. I think Luna and River is that this trope is supposed to be about.
I think two tropes are struggling for expression here.
One is about a non-romantic Manic Pixie Dream Girl, a Cloud Cuckoo Lander whose strange ways are played for cuteness. Think Dharma from Dharma and Greg, or what Rin appears to be in the first act of Katawa Shoujo.
The other is a someone who is in touch with the supernatural, or thinks to be. No superpowers, and often kept ambiguous. A variant of the Granola Girl.
In both cases, they are not the protagonist, play a foil to the more Straight Man protagonist, and are usually girls. Do we have either of those covered elsewhere?