How do the Evas activate even when they run out of power?

[Hoshikawa-kun]

I would say that the lack of explanation for unpowered movement is part of the story. Ritsuko certainly doesn't know how the Evas seemingly circumvent physics at their whim, and nobody has enough time to figure it out in the series. It's actually realistic for some functions to go unexplained.

There are two states to a machine--the machine when it's rolled out of the factory, completely new and ready to operate like any other mass produced model of its kind, and the state the machine is in after it's been used for some time. In the second state a machine develops unique kinks and does some unexpected things; aircraft might be capable of something they weren't designed for, a computer spontaneously falls through a logical loop, a car's door locks become temperamental, and so on. Likewise, the Evangelions will develop their own individual oddities, and while there is a way they achieve those oddities, it's not one that we know.

Moving without any logical power source is certainly a leap from moody door locks, but everything is scaled up with the Evangelions. As with any machine, the Eva's imperfections humanize them.

[Hawq]

So how does eating the angel allow the Eva to suddenly grow an S2 organ...?

I'll put on my helmet before typing this bit, I always had the vague theory it already had one (bear with me folks) but that it didn't function properly & upon eating Zeruel's engine it got the parts needed to regenerate it, well we know its different to the rest (I won't give my opinion here as one helmet donning bit is enough for now) & with the unit 4 test to use one who's to say they didn't try before. Of course maybe it just ate it & absorbed it, if you can rip the enemies arm off & regrow yours with it then why not that I guess. & before anyone mentions unit 2 going off in End I never claimed there weren't holes in the thought, just that it was a thought along the lines of the quoted bit