A quick Schwartzian Transform does the trick. Your sample is not an array of arrays BTW. I guess you are tired.

@in = (                                 
        [qw(M N)],               
        [qw(M N Q P O)],                          
        [qw(C B A)],                           
        [qw(U S)],                               
        [qw(V T)],                            
        [qw(C G F E D)],                       
        [qw(C G F H)],                         
        [qw(C G F H I)],                         
        [qw(C G F H J)],                         
        [qw(M K)],                              
);  


my @out =  map{$_->[0]}  sort{$a->[1] cmp $b->[1]}  map{[$_, concat($_
+)]} @in;

sub concat {
    my $ary = shift;
    $ary = join '', @$ary;
    $ary =~ s/\s//g;
  return $ary;
}

use Data::Dumper;
# munge the output for compactness and to make it look nicer
$Data::Dumper::Indent = 0;
print map {s/\[/\n        \[/g; $_} Dumper \@out;

__DATA__
$VAR1 = 
        [
        ['C','B','A'],
        ['C','G','F','E','D'],
        ['C','G','F','H'],
        ['C','G','F','H','I'],
        ['C','G','F','H','J'],
        ['M','K'],
        ['M','N'],
        ['M','N','Q','P','O'],
        ['U','S'],
        ['V','T']];
[download]

cheers

tachyon

s&&rsenoyhcatreve&&&s&n.+t&"$'$`$\"$\&"&ee&&y&srve&&d&&print