There is no doubt that Asuka likes Shinji, but does Shinji like her?
>inb4 he saved her from falling into volcano
He would have saved anyone
>but he told her she is the only one for him in eoe
He crawled to her only in the very end, because all other options were unavailable and strangled her when she refused.
Shinji is extremely selfish, he doesn't give anything and expects a lot in return. The only person Shinji cared about was Kaworu, because he gave him unconditional (and unrealistic) love