Mystical Waif: She's a Shichikouhouju, one of the most powerful and legendary Edel Raids. Of course this means that everyone wants their hands on her. She's frequently rendered helpless and constantly protected by the main character. Personality-wise, she fits the mysterious and distant part.
Phlebotinum Girl: Female love interest with non-human origins and special powers that make other characters seek to possess her, which initially depresses her and makes her detest humans. She's also physically frail and frequently weakened by the use of her abilities.
Rei Ayanami Expy: Blue hair? Check. Pale skin? Check. Quiet and deeply emotionless demeanor? Check. Not exactly human? She's an Edel Raid, which allows her to turn into a weapon. Mystical Waif? Check. Weak physical condition with a recurring need to be looked after? Check. Defrosting love interest? Double check. Her name is even one letter apart from Rei.
Shapeshifter Weapon: She's an Edel Raid, girls who can bind their soul with their Pledger and turn into a weapon.