Who's talking to who encryption - does this concept work?
Like @StephenTouset said 


  You appear to be reinventing the concept of onion routing.


For a practical example, check the Tor Project (based on the Onion Routing program) which enables online anonymity and directs internet traffic through a worldwide network consisting of thousands of relays to conceal a user's location… which would cover most of what you need.

But there are other implementations out there too; most of them handling encrypted, anonymous data (voice, text, binary) transfers using random node allocations and bridging.

Besides that, it is worth diving into mixnets too.

For more, the anonymity bibliography might come handy as an orientation for further research.