You need to remove the clause STRICT according to the documentation :

*...RETURNS NULL ON NULL INPUT or STRICT indicates that the function always returns null whenever any of its arguments are null. If this parameter is specified, the function is not executed when there are null arguments; instead a null result is assumed automatically...*

Use your code like this:

CREATE OR REPLACE FUNCTION pl_test_function(mand_arg varchar
                                          , opt_arg1 varchar DEFAULT NULL
                                          , opt_arg2 varchar DEFAULT NULL) RETURNS void AS 
$$
BEGIN
      INSERT INTO pl_table (mandatory, option1, option2) VALUES
             (mand_arg, opt_arg1, opt_arg2);
END;
$$
      LANGUAGE plpgsql ;

You need to remove the clause STRICT according to the documentation :

...RETURNS NULL ON NULL INPUT or STRICT indicates that the function always returns null whenever any of its arguments are null. If this parameter is specified, the function is not executed when there are null arguments; instead a null result is assumed automatically...

Use your code like this:

CREATE OR REPLACE FUNCTION pl_test_function(mand_arg varchar
                                          , opt_arg1 varchar DEFAULT NULL
                                          , opt_arg2 varchar DEFAULT NULL) RETURNS void AS 
$$
BEGIN
      INSERT INTO pl_table (mandatory, option1, option2) VALUES
             (mand_arg, opt_arg1, opt_arg2);
END;
$$
      LANGUAGE plpgsql ;