What's going on is during episodes 25-26, we're getting direct insight into the mind/heart/soul of Shinji, Asuka, Misato, and possibly Rei also, with the majority of it being Shinji.
The thing to focus on here is the thematic insight of what is happening...concerns of "where are they?" "how did they get there?" "what is happening?" "Who is asking these questions?" are supposed to be immaterial. What's important to understand is that these episodes focus on the fact that these characters, and by empathizing, everyone, feels insecure, scared, and lonely, desiring to feel good about who they are, and to love and be loved...chiefly through interacting with other people.
The last few minutes of the last episode are cathartic for Shinji, because he finally realizes that relying on external validation of his existence is a fool's game...he doesn't need other people to say that he's worthy of being, he just needs to believe he is. Not coincidentally, it's when he finally feels this way about himself that everyone in his life suddenly appears and congratulates him...again, that's not meant to be taken literally; it's symbolic that how you feel about yourself is what you receive from others...you get back what you put out.
I personally found this to be an incredibly uplifting message, and was deeply moved...all the moreso for the fact that I can draw strong parallels between myself and Shinji. For him to be able to overcome his own inner demons like that and self-actualize by declaring that he knows he's a good person worthy of continuing on in this existence, I saw the same thing for myself. I think (and this is totally just my opinion), that that's the meaning of life...that we set our own meaning; we're all as happy or as unhappy as we set our minds to being. "Life is painful - suffering is optional" is another way of saying it.