How can I determine the edition an Oracle session is using?
Query V$SESSION and include the column SESSION_EDITION_ID which contains the value you are looking for.  

The link http://docs.oracle.com/cd/E11882_01/server.112/e40402/dynviews_3016.htm#REFRN30223 defines all the column meanings for that dynamic view; I would probably do a query like 

SELECT SID, USERNAME, SCHEMANAME, OSUSER, 
   PROCESS, MACHINE, TERMINAL, PROGRAM, 
   SESSION_EDITION_ID 
from V$SESSION  
order by SESSION_EDITION_ID;