As for the reason why Shinji choked Asuka, I stick with the translation of “Kimochi warui” card from Eva card game, but I’m willing to accept other theories,
Shinji renounced the world where all hearts had melted into one and accepted each other unconditionally. His desire… to live with ‘others’ — other hearts that would sometimes reject him, even deny him. That is why the first thing he did after coming to his senses was to place his hands around Asuka’s neck. To feel the existence of an ‘other’. To confirm (make sure of) rejection and denial.
But I have no clear explanation of why did Asuka caress Shinji when he is strangling her.