Hello,
I noticed that there was a lot of questioning about whether or not Java would run on the Intel Edison.
I asked a representative of Intel at Maker Faire NYC if Java would run on it, and the response was "We haven't tried it, but I don't see why it can't."
I have been able to download the Linux i586 version of the JDK (7u67) from Oracle and run it without issue (read: I can get the version).
I hope this clears the air for anyone else wondering.
Thanks for reading,
Billy K