I agree with Beth. I have developed a product based on the same thought process. I have a java server running on a socket, which has a client library that client app's use to connect to the server. The client abstracts out the socket piece and provides easy api's for client apps to call.
The server is equipped to handle multiple client connections in parallel, thread pool concept.
Now, since it will be a java client library, you can only run this on android. To get this working on other platforms, you can run this client piece on J2EE. This way you create a third middle layer. All other platforms can then connect using the browser.
With this done, you can now use JSON to Object libraries to expose your object (on the server side) to JSON. I haven't done this yet, but will do it in a few weeks.
Btw, I just cant get myself to use any cross platform frameworks. They promise the world, and dont mention any of their limitations upfront. Its painful towards the end of your product/app release to find out all these limitations/hidden costs.