Current isolation level in oracle
Using the query from the SO answer Vincent Malgrat referenced, here is how you can get the transaction isolation level for the transaction in progress:

SELECT s.sid, s.serial#,
   CASE BITAND(t.flag, POWER(2, 28))
      WHEN 0 THEN 'READ COMMITTED'
      ELSE 'SERIALIZABLE'
   END AS isolation_level
FROM v$transaction t 
JOIN v$session s ON t.addr = s.taddr AND s.sid = sys_context('USERENV', 'SID');


If you are not already in a transaction you can start one with the following:

declare 
   trans_id Varchar2(100);
begin
   trans_id := dbms_transaction.local_transaction_id( TRUE );
end;
/


It seems like there would be an easier way than this.  I don't know how to get the default isolation level for the session if that is what you are looking for.