What I'd like to propose (and I'm sure I'm not the first) is that it's the EVA units themselves as the 4 Adams, presumably set up by Gendo and Nerv or Yui or whoever. Unit-01, Unit-00, Unit-02, and Unit-08 (assuming it's not some 01 update or something) were to be made gods - or the vehicles in which godhood was attained and said power was used. Only, as Gendo says in the provided screenshot,
Unit-01 has had this power activated prematurely, before the other Units could do the same. I left out Unit-06 because that's SEELE's secret weapon and not part of the plan. Unit-07 is a mystery to be discredited.
This can even mesh with the "Children are the Adams" thing as well, seeing as how Kawuro would still be part of SEELE's own plan and the Nerv children (and Mari) would be piloting the aforementioned EVA units. The biggest problem with this is that, as it looks now, Mari is also not part of Nerv's/Gendo's/Yui's plan, and thus that leaves us with only 3 of the "Adams"...unless you believe Yui or Gendo had any idea of Kawuro in which place he'd take the spot of the 4th.[/spoiler]