use strict;
use warnings;

sub r(&$@) {
   my $cb = shift(@_);
   my %seen;

   local *_r = sub {
      my @v = @_;
      return if $seen{join $;, @v}++;
      return if not $cb->(@v);
      return if @v == 1;
      for (0..$#v) {
         my @v_ = @v;
         splice(@v_, $#v-$_, 1);
         _r(@v_);
      }
   };

   _r(sort @$_) foreach @_;
}

r { print(@_, "\n"); 1 } [ qw( A B C D   ) ],
                         [ qw( A B C E   ) ],
                         [ qw( A B C F G ) ];
[download]

Output:

ABCD
ABC
AB
A
B
AC
C
BC
ABD
AD
D
BD
ACD
CD
BCD
ABCE
ABE
AE
E
BE
ACE
CE
BCE
ABCFG
ABCF
ABF
AF
F
BF
ACF
CF
BCF
ABCG
ABG
AG
G
BG
ACG
CG
BCG
ABFG
AFG
FG
BFG
ACFG
CFG
BCFG
[download]

Both the implementation and the algorithm can surely be improved.

Update: The code block now returns a value. This allows the option to skip, as desired.
Update: Slightly modified to attain your ultimate goal.
Update: (Bug fix) Added sort.
Update: I can't think of another algorithm. This will likely be my last solution.