These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Rei practically rewrote the book on this trope. According to the author:
Gregg: Rei isn't just a nephilem, she's of a batch of Nephilem created for the purpose of killing. Basically, she's a Nephilem super-soldier that Naoko made to murder two people and a lot of collateral. What Yui and Gendo have done is taken what's basically homicidal mania and focused it into being crazy awesome.
This version of Rei has been titled "Terrifying!Rei", as contrasted with Aeon Natum Engel 's "Creepy!Rei" or Shinji And Warhammer 40 K 's "Apocalypse!Rei". Additionally, Terrifying!Rei's sisters are referred to as the Ree, through an exceptionally dubious application of the English rules for pluralisation. Each has her own name.
Mini!Sandalphon is officially called "Junior". The Ree demanded that he be named "Wuffles" and made their pet. In the forum thread, "Wuffles" has stuck.
The Nobody Dies version of Gendo has been (almost) officially named "Gendo McBadass" and his sheer awesomeness in comparison to his Canon self has set of several rounds of "Brofists" and Epic Hamminess from the forum goers.
Zeruel has become known as Big-Z following his arrival on Earth at the end of Chapter 65.
Fridge Brilliance: When Mari gets resurrected from the MAGI and is revealed to be the remnants of Ramiel, she is called Rami by other Angel-spawn, which is an anagram of her name.
Leliel joins up with NERV because, since she can go through many alternate universes through the Dirac Sea, she knows that she will die a horrible, gruesome death if she let events happen like canon, and has decided the best strategy is join them while there is time.
And then in chapter 66: Shinji is a nephilim — complete with the blue hair and red eyes. In other words, he has becomeKamina.
Misato, at the end of Chapter 106, when everyone explains the full situation to her, realizes that in the last half of the chapter, she figuratively mooned her HSQ as she went by, going at an appreciable fraction of lightspeed.
"I fucking raced the fucking Stig and blew him up with my transforming super car which has a jet engine and an Evangelion AI."
Hype Backlash: Season Four saw an increasing number of complaints in the forum about various issues with the fic, mainly due to the opinion that the things which made it awesome in the first place are getting completely out of hand.
I Knew It: Not an uncommon reaction to Ichi turning out to be Shinji's little sister.
Iron Woobie: Canon!Shinji. Gendo sums it up pretty nicely in chapter 44.
Gendo: I don't know if this means anything since I'm not, technically, your father...but I am proud of you. I don't know if I could turn down paradise.
Jerkass Woobie: Kei started off as a particularly cold and calculating version of the former, but is slowly transitioning to the latter as things keep derailing her original plan and shaking her emotional balance.
Rei and Hikari show signs of being heroic-examples-in-training of this with their awesome plot to blackmail the school principal and bolster Asuka's self-confidence simultaneously.
As of ch.35, Gendo has revealed his Magnificence. After all, one does not simply start a Bar Brawl at a state function, fight the President of the United States to a mutual KO, and then BS a convincing enough explanation to not only stave off death via angry wife, but actually get her in the sack, unless one is a true Magnificent Bastard.
Gendo: (to Shinji) Watch and learn.
Misato has proven quite nicely that she can make a plan come together.
"We nailed the mother of all humanity to a cross in an attempt to make her STOP CALLING US AND ASKING IF WE'RE EATING RIGHT AND WHEN WE'RE GOING TO FIND A WOMAN TO SETTLE DOWN WITH." Babies. Babies. Babies babies babies babies babiesbabiesbabiesbabiesbabiesbabiesbabiesbababies
Shinji becomes this due to being the only person conscious after the Function Brawl.
The Ree. Even among them, Kiko and Zyuu stand out.
It was barely implied in chapter 51, but the idea of Israfim/EVERYTHING has become very popular on the forum.
Terrifying!Rei (AGAIN!) has a short list of her own variant of Chuck Norris Facts, and has everyone on the forum (wisely) terrified of her and her feats, which include breaking the fourth wall and reality in order to threaten play with her new bestest best friends online!
Which has spawned such memetic gems as "[Insert Problem/Item/Event]? Drop the Sun on it," and "Eat Sandwich, [Insert Improbable Event]."
In-universe example: After Gendo started a bar brawl with the entire body of representatives of the governments in Geneva, Shinji was the only conscious person, sitting on his metal folding chair when the security arrived. Someone made a Shinji Facts website after news of the incident spread.
For some reason, Spacebattles has constantly mentioned a certain stage from Mega Man X2 ever since the beginning of the Asuka vs the WorlDINOSAUR TANK
Whenever Kaworu is brought up - Tabris is F___ing gay.
Mind Game Ship: Annette's parents (Shinji's uncle and aunt, making him wonder if a fetish for intellectual duels runs in the family), first met in a chess park and after four hours of playing, got rather intimate.
Kei making the Everybody Dies scenario may count, especially if you're one of The Ree...
As if what Iruel did to Ichi wasn't bad enough, there's also taking Asuka's fantasy where she was an empowered superhero and turning it into the girl's mother cutting her up for body parts. Thank God for Reip.
Shinji: You have succeeded in doing what no other Angel has done. You have pissed me off.
It's revealed that the difference between this version and Canon!Yui is that she didn't cross it. That being said, due to certain revelations, she has gotten dangerously close to this, although we won't know for certain until her ultimate plans are finally revealed.
The main reason why "Terrifying!Rei" is so terrifying, despite her general cheerfulness and friendliness. Well, that and the destroying-cars-with-squeaky-mallets thing. That and she's also an artificial being created by Naoko Akagi to kill Shinji...at least, according to Yui.
The Ree, or at least most of them, take this a step further through their behavior and personalities, which are even more outrageous than Rei's.
Despite Yui being alive, Shinji still spends the better part of his life raised by his aunt and uncle, albeit with his parents still involved in his life. In the first few chapters, he says he hasn't seen his father in person in three years and his mother in five. It is implied that Yui is so concerned with the children of other people that she handed off her son to relatives. And then there is Kyoko's raising of Asuka, which falls under Abusive Parents at best. Additionally, Yui is not portrayed as a saint and instead as just as manipulative as Gendo.
That being said, this doesn't seem to bother Shinji as much as it did in canon. In his own words:
Shinji: (To Uri) My parents don't win awards either, but I do know that my mother, at least, made sure I could stand up on my own two feet if I had to. I'm seeing a lot less of that in your family.
There's also the fact that one of Maya's primary characteristics seems to be that she's a lesbian. It's not the fact that she likes girls, it's the fact that she likes girls is one of the first things we learn about her —in a list of entirely unrelated character traits — and she is later described as "the resident combat lesbian", despite being both closeted and one of the Bridge Bunnies.
And apparently being a lesbian is enough for her to not be affected by Shinji's accidental Chick Magnet powers in ch. 72, despite that not making sense with how they're described (only excluding females who wouldn't produce viable offspring).
The Untwist: Oh come on, a name like Uriel, plus white hair and partially red eyes, and then we're supposed to be surprised when Uri turns out to be part-Angel?
What an Idiot: Shinji gropes Asuka in order to get Uri to punch him, which would reset his core. It works, but Shinji expects Uri to calm down... which he doesn't.
Asuka. Regardless of your opinion of her canon counterpart, you will want to give her multiple hugs before this fic is over. She's now the one who talks to the infamous doll, not her mother, asking it for advice and sobbing her heart out to it. And then it answers back...
Iruel actually calls her this when he reveals himself to her in ch. 37.
Of all people who would get a moment like this, you'd never expect one of the Ree. Turns out that the primary reason they're kept locked up isn't for the safety of human civilization, but because their S2 organs are unstable. Whenever an Angel appears, this condition is aggravated to the point where they would die unless given immediate specialized treatment, and that's just the best case scenario. Worst case, they turn into an Angel and start murdering everyone around them. Learning this puts their confinement into a whole new light.
They don't have to worry about this anymore. All of their S2 organs are stable now. RUN.
Even after this, Iti remains the most Woobie-ish of the Ree.
00-Em has seen all his "siblings" deleted by SEELE, his sister is thinking herself to death, he's growing more aware of just how broken he and his sister really are, and as of the end of the story, he's seen his sister seemingly die, then transform into a monstrous Grigori/Angel/Nephilim hybrid, seemingly die again, and then be trapped inside the remnants of said monstrosity in a near-death state. If you don't feel a little bit sorry for him, then you have no heart.