Current isolation level in oracle How to get the current (default) transaction 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.