I don't speak Java, but - while you wait for another (i.e. better) answer, read this.
SET is SQL*Plus command, while stored procedures (SP) are PL/SQL ... well, procedures. That's why SET SERVEROUTPUT ON (SSO) won't work; besides, I believe you do not have SSO in the SP, do you? Such a procedure wouldn't compile.
Here is DBMS_OUTPUT package manual (Oracle 8, but never mind; what is your Oracle version, anyway?). It says that one should use DBMS_OUTPUT.ENABLE in order to enable output (obviously); it is not necessary to call it if you use SSO in SQL*Plus.
However, as you use Java and not SQL*Plus, you might try with it.
Furthermore, where do you use DBMS_OUTPUT? Is it in an exception handling section, perhaps? If so, avoid it and use RAISE_APPLICATION_ERROR instead - it doesn't depend on SQL*Plus, Java or whatever else.
Finally, read this Ask Tom article; perhaps you'll find it helpful.
Hello, Shammat! Next time wait until I finish my dummy answer, and then give the proper answer