Witchfinder General said:
From what I remember - and it's been a long time - Shinji is given the chance to give the human race a new beginning and essentially recreate the world for the greater good but Shinji being the screwed up individual that he is squanders the oppurtunity and fails.
Nope, totally wrong. Shinji, for one brief moment, essentially becomes God. He has the choice of accepting or rejecting Human Instrumentality.
SEELE believes Instrumentality is the next step in evolution, but logically speaking, it's just a return to the nothingness before creation, bodiless souls and a primordial soup.
Gendo correctly believes that he can manipulate Instrumentality and see Yui again if he can become "God" and merge with Unit 01. Rei III shuts down his plans and gives this power to Shinji instead.
Shinji initially makes the wrong choice, to end all humanity and initiate Instrumentality... the resultant Anti A.T. field causes all life on the planet to lose form and substance, just as Shinji did in his Evangelion entry plug when he goes to a 400% synch ratio and Unit 01 goes Berserker, just as Asuka does when Unit 02 goes Berserker just before the lances kill it (and thus, Asuka survived).
And thus we enter into the simultaneous Episode 25 / 26 & End of Evangelion trippy mindphuckery phase of the story, where Shinji finally learns the value of individuality and rejects instrumentality.
The Beast That Shouts "I" at the Heart of the World, indeed.
Lillith-Rei is destroyed, freeing all the souls.
Shinji and Asuka are the first to reform themselves, but anyone else can, too. Presumably, this only applies to characters that weren't already dead, but this is a fine point and doesn't really matter a whole lot.
As for why Shinji strangled Asuka? Well, he did the same thing in his nightmares during Instrumentality and I'm thinking his fractured mind didn't really know the difference between the strange reality he found himself in and his own nightmares, so he lashed out, just as he lashed out at the Asuka in his nightmare. And then she caressed his face, finally showing him kindness, and then just out of pain and guilt and whatever else, he just stopped and began sobbing.
And then she said "I feel sick."
Frankly, I still don't get the "I feel sick" thing, not completely. I think with regards to both characters, Shinji and Asuka, the author is trying to hammer home his whole point.
What is his whole point? It's complex. It's something like "Reality sucks sometimes but it's better than living wholly in a dreamworld or living in a world where there is no identity or individuality. Therefore, even pain and misery have their worth because they're a valuable part of the human experience and accepting that reality is not only part of maturity, but it helps you appreciate the good things in life more."
It may seem somewhat trite to some, but it still seems pretty deep to me, and actually a worthwhile moral-of-the-story for a deeply depressed Otaku, as I was when I first watched it.