Update: My sets can overlap too. For exmaple I may have 4 sets like '0..7','1-6', '6-12',and '3..9'.

You don't say how many from each of those four sets, so I did 2 from each, but it should be obvious where to change the numbers supplied to permuteSets for different requirements.

The following runs in 1.7MB and takes a few seconds for wc -l to count the results:

#! perl -slw
use strict;

sub nFor(&@) {
    my $code = shift;
    die "First argument must be a code ref" unless ref( $code ) eq 'CO
+DE';
    my @limits = @_;

    my @indices = ( 0 ) x @limits;

    for( my $i = $#limits; $i >= 0; ) {
        $i = $#limits;
        $code->( @indices ), ++$indices[ $i ]
            while $indices[ $i ] < $limits[ $i ];
        $i = $#limits;
        $indices[ $i ] = 0, ++$indices[ --$i ]
            while $i >= 0 and $indices[ $i ] == $limits[ $i ];
    }
}

sub permuteSets (&@) {
    my $code = shift;
    my @subsets;
    while( @_ ) {
        my( $n, $set ) = ( shift, shift );
        push @subsets, [];
        nFor { push @{ $subsets[-1] }, [ @{ $set }[ @_ ] ] } (scalar @
+{ $set } ) x $n;
    }
    nFor{
        $code->( map{ @{ $subsets[ $_ ][ $_[ $_ ] ] } } 0 .. $#subsets
+ );
    } map scalar @$_, @subsets;
}

permuteSets{
     print join '-', @_;
} 2, [0..7], 2, [1..6], 2, [6..12], 2, [3..9];

__END__
C:\test>965138 | wc -l
5531908

C:\test>965138
0-0-1-1-6-6-3-3
0-0-1-1-6-6-3-4
0-0-1-1-6-6-3-5
0-0-1-1-6-6-3-6
0-0-1-1-6-6-3-7
0-0-1-1-6-6-3-8
0-0-1-1-6-6-3-9
0-0-1-1-6-6-4-3
0-0-1-1-6-6-4-4
0-0-1-1-6-6-4-5
0-0-1-1-6-6-4-6
0-0-1-1-6-6-4-7
0-0-1-1-6-6-4-8
0-0-1-1-6-6-4-9
0-0-1-1-6-6-5-3
...
7-7-6-6-12-12-9-6
7-7-6-6-12-12-9-7
7-7-6-6-12-12-9-8
7-7-6-6-12-12-9-9
[download]

I also need to eliminate duplicate items. In the case of overlapping sets, every resulting row should satisfy the initial condition.

I don't suppose you'd care to describe the application?

AFAIK, there in no combinatorics algorithm that would address those requirements, so it is going to be a post-production step and is left as a exercise.