If your hash is really big, you could speed things up by using a Schwartzian transform sort:

 #--snip -- Hash declaration omitted --
#--  Schwartzian Transform Sort --
my @sorted=  map{ 
                $_->[3] 
            } sort{ 
                $a->[0] cmp $b->[0]  
                || 
                $a->[1] cmp $b->[1]
                || 
                $a->[2] cmp $b->[2] 
            } map{ 
                [ @{ $myData{$_} }{qw| Category File Name | },$_] 
            } keys %myData;
   print join (", ",@sorted), "\n"; 

#Prints: Method2, Method4, Method3, Method1
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Update:On second thoughts - this is probably a marginal gain in efficiency - array access Vs. Hash value fetch.