Haven't gone through this thread yet, but it looks like most of this stuff everyone already knows.
Firstly, like NONE of the stuff from the preview at the end of 2.0 is in this movie. Secondly, there's some bizarre stuff, like the floating battle ship and all the red stuff shaped like Evangelions and everything seems like an Angel (not literally but there's pattern blues everywhere it seems), but mostly this magical floating battleship that seems to have come out of nowhere.
We start off with the space battle, but it's not so much a battle as it is Asuka recovering this black cross with a Nerv logo on it, I assume that Shinji's inside this thing. At some point there's an angel and a fight ensues. Mari and Asuka are both fighting, Mari in the pink one, and at some point, because she has no thrusters, her Eva falls back to earth. She's got a gun that looks like a 50cal.
Upon returning, Shinji wakes up and realizes he's the most hated person on Earth. Everyone hates him, except maybe Toji's sister (who is the brown haired girl from the new trailers). Misato hates him, Ritsuko's got short hair, the other new characters are the new bridge crew, the bridge of this wacko floating battleship, and they all work for (IIRC) Wille? Not Nerv. Shinji's an idiot and doesn't understand why everyone hates him. He's relieved to see Asuka again but she hates him too. They're all out at sea, and it looks like there might have been another angel attack. Eventually, Rei shows up in Eva-00 (or was it 09?), busts Shinji out of jail (he's wearing some sort of collar that can explode), Misato wants to use the collar but can't.
They all go back to Nerv, which is all kinds of fucked up. There they find Kaworu who plays the piano a lot. Gendo is now sporting a visor kind of like Keel. Shinji realizes that Rei isn't the same as before, he's also really mopey and befriends Kaworu, who somehow teaches Shinji how to play the piano instantly. Kaworu also fixes Shinji's SDAT, also, he takes the collar off and puts it on himself. Shinji eventually hangs out with Fuyu who tells Shinji all about what happened to Yui (she's got wings during the contact experiment) and what happened when he tried to save Rei, pretty much why everyone hates him. So there's also Eva-13, which kind of looks like Eva-01, it's in some sort of containment because it seems Misato's people can detect activated Evas.
When Eva-13 is activated, Kaworu and Shinji both pilot it from separate entry plugs, but they can see each other, as if they're sitting next to each other. This instantly sounds the Misato alarm and they send Asuka and Mari to deal with it. They descend through central dogma (some weird CGI during this part, not sure what was going on with all the blocks and the floor) until they eventually reach Lilith, who looks in bad shape. There's what looks like Eva-sized skulls everywhere. There are also 2 spears (one is Longinus and the other is, forgot the name, was mentioned in this subforum), one is stuck through Mark-VI and the other looks like it's just sticking in Lilith. Shinji is told that if they get the spears they'll be able to undo all the crap that Shinji did via 3rd Impact. Kaworu's suddenly not so sure, I think he says the spears are in the wrong place or that someone's messed with them, he's sitting around wondering what was up while Shinji fights Asuka, Rei is down there also with her Eva and is in the battle. Asuka runs out of power, so Shinji gets the two Spears, and what do you know, 4th Impact starts. But Misato and the floating battle ship shows up and tries to stop it, the battleship's guns can pierce AT-Fields. Rei's Eva turns out to be Seele controlled and starts attacking the battleship, hacking into its systems, it seems it's also an Angel. Asuka activates some sort of "beast mode" and takes it out, Rei's entry plug is ejected. At some point, the collar explodes and Kaworu is turned into hamburger meat, Shinji's pretty upset about it and at this point, he's just a dead heap. His entry plug is ejected, Asuka has to self destruct so she ejects. The battleship is saved and 4th Impact is averted, though it looks like Earth is pretty bad off. The movie ends with Asuka pulling Shinji out of his plug, he's completely unresponsive, and they and Rei walk off.
Probably missed a lot of the details, but I'm sure all the other synopsis from the thread can fill those in. Not sure how I feel about this one, I definitely enjoyed it but there's a lot of questions/loose ends. I'll have to wait for a full translation of the dialogue before putting together any critical thoughts. Some of the stuff that kind of bugged me was the battleship, which seemed to have come out of nowhere, and Shinji being pretty much an idiot throughout the entire movie.
The next time preview has an Eva that looks like the pink Eva and Eva-02 stiched together fighting a bunch of other Evas that all look alike, probably an Eva series? They don't look like harpiess though.