The Master's Sun - she can see ghosts and has kind of lost her sense of embarrassment
Jealousy Incarnate - Gong Hyo Jin just seems to like playing characters that lack a bit of self awareness; similar to tMS, in this one her character is also not very good at respecting normal boundaries in relation to the ML (it ends up helping him in the end)
Sound of the Desert - she was partly raised by wolves
Hi! School - Love On - she's an angel-turned-human
W - she has to behave pretty strangely to deal with even stranger circumstances
The K2 - she grew up hidden from the world by her family and she has a form of social phobia + experiences panic attacks when exposed to flashing lights
Madame Antoine - she tells fortunes in her cafe and pretends to be visited by the spirit of Marie Antoinette
Healer - she's a very loveable free spirit, most of her friends are ex-convicts (her dad is a criminal defence lawyer / coffee shop owner), and she experiences panic attacks when faced with certain violent situations
Flower Boy Next Door (I didn't finish this) - the FL is a shut-in
I haven't seen it, but from what I've heard about it, My Girlfriend is a Gumiho also probably fits. In some of these the ML also isn't just a completely normal, average guy, but for the most part they're not too weird.
