The way I see it is that Shinji strangling her is either to verify reality, that she is in fact there, and/or to verify that she has the will to live....
Asuka reaches up to Shinji, at which point he stops strangling her. This is her verifying, to him, that she is real and has the will to live. When Shinji sees this, he lets her go and begins to cry, perhaps due to joy at not being alone, joy that Asuka is alive (Since he saw Eva 02 in such a mangled state), or perhaps the weight of everything he's seen and been through finally spills over, now that he has someone for him to cry to.