You should take a look at Threema. That does exactly what you describe afaikt - except XMPP, its a walled garden - using NaCl.

Edit: I should probably elaborate:

- It uses the internet connection to transfer messages

- You can choose not to publicize your phone number and solely exchange keys via QR-codes.

- It uses NaCl which utilizes a permanent Diffie-Hellman key exchange to derive a symmetric key for authenticated encryption. If you can decrypt your messages, then you can forge them.

- There is no desktop client yet, but it is on the far agenda.

- It is not an open protocol.

Personally I don't think XMPP is a good basis for an asynchronous, encrypted network protocol. It is extremely verbose and the extension that would make it tolerable to use with unstable internet connection and multiple clients are not supported by enough clients and servers. Also it misses an encryption standard for asynchronous communication. And again I think OTR is not a good basis for that. For example afaik there are no mechanisms for recipient key selection in a non-interactive way.

PS: I would greatly appreciate some markdown dialect for the Hacker News posts, if only to typeset lists.