Rebuild of Evangelion-2 primarily follows the canon of the Rebuild series with additional information seeded from the original animated series. The plot differs significantly after Zeruel. The third impact is actually more like another second impact and the world is pelted by cheap mockup angels.
Gehirn turns into paramilitary organization Nerv which makes a GeoFront within a crater on Earth. SEELE, an organization of shadowy characters manages global economic and political affairs. Evangelion units produced from Nerv protect a civilian/militarized society from Angels, beings trying to come in contact with Lilith to create the third impact.
Shinji returns to Tokyo-3 to pilot Eva Unit 01 and reflects upon his purpose in the world. Gendo Ikari controls Rei Ayanami in an attempt to influence the Human Instrumentality project and it ultimately fails. After the third impact, Nerv is crippled and Gendo Ikari killed.
The Evangelion pilots remain to fight cheap mockups of Angels spawned from the Angel of the Womb, Armisael, for several years.