Is this really what you mean?

(
    (
        ( not defined($pname) ) 
        and 
        ( $pname eq '' && defined($policy_ur) )
    )
    and $policy_ur eq ''
)
and 
(
    not (
        defined($odate) && $odate eq''
    )
)
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Please take the time to read about operator precedence. That perl has logical operators with two levels of precendence is very useful, but it is a trap for the unwary or unaware.

If you don't pay attention to precedence you'll think the answer to 2+3*5 is 25. Even worse, if you have code to implement X+Y*Z that uses bad precedence, and you test your code with X, Y and Z all being 1, you'll believe the code works. Then six months later, Bob in accounting is wanting to know where $5 million went...