Woke up this morning thinking it could be much simpler. This time I do use a numeric sort:

#!/usr/bin/perl -w

use strict;

my @unordered = qw( 
  2HB 3HB C CA CB CG CD1 CD2 CE1 CZ CE2 HE2 HE1 HH HD1 HD2 N O OH
);

# change weighting
my %main = (
  N => 1, CA => 2, C => 3, O => 4, 
  S => 100, P => 200, H => 1000,
);

my %greek = (
  B => 1, G => 2, D => 3, E => 4, Z => 5, H => 6, 
);

sub sortable {
  my $atom = shift;
  $atom =~ /(\d)?(N|CA|C|O|S|P|H)(B|G|D|E|Z|H)?(\d)?/;

  # we may have empty groups, so quiet warnings
  no warnings 'uninitialized';

  # make a number that sorts
  # keep parts at different orders of magnitude so they don't conflict
  $main{ $2 } 
    + ( $greek{ $3 } * 100 ) 
    + ( $1 * 20 )
    + ( $4 * 10 );
}

# operator changed to numeric comparison 
my @ordered = sort { sortable( $a ) <=> sortable( $b ) } @unordered;

print join "\n", map { $_ ."\t". sortable( $_ ) } @ordered;
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Gives:

N       1
CA      2
C       3
O       4
CB      103
CG      203
CD1     313
CD2     323
CE1     413
CE2     423
CZ      503
OH      604
2HB     1140
3HB     1160
HD1     1310
HD2     1320
HE1     1410
HE2     1420
[download]