Error calling stored procedure from trigger in Oracle Database 11g
Your trigger doesn't need the CALL keyword.  

create or replace trigger TRYTABLE_BEF_UPD_ROW
before update or insert on TryTable
for each row
begin
    TryJavaHelperRun(:new.arg1, :new.arg2);
end;
/


Generally, you should never use CALL in a PL/SQL block-- just execute the procedure.  I assume that CALL is some ancient leftover syntactic remnant from some ancient version of Oracle.  It allows you to replace the entire PL/SQL block that is the trigger body with a single CALL statement, i.e.

create or replace trigger TRYTABLE_BEF_UPD_ROW
  before update or insert on TryTable
  for each row
  call TryJavaHelperRun(:new.arg1, :new.arg2)
/


Personally, I've never come across a case where there was any benefit to ditching the "normal" PL/SQL syntax in favor of using CALL in a trigger.

This assumes that you can call the TryJavaHelperRun procedure successfully in general.