There are two parts to the puzzle - how to sort a large file, and how to merge multiple large sorted files. Super Search will help with the first part. The second part is achieved by reading a record from each file then outputting and replacing the smallest record in the current set until all records have been processed. Something like:

use strict;
use warnings;

my $data1 = <<DATA;
1
3
7
10
29
DATA

my $data2 = <<DATA;
2
4
11
20
22
24
30
DATA

my $data3 = <<DATA;
90
DATA

my @files;

# Open files and add them to the list
for my $inFile (\$data1, \$data2, \$data3) {
    push @files, [];
    open $files[-1][0], '<', $inFile;
    
    my $fh = $files[-1][0];
    $files[-1][1] = <$fh>;
    
    if (!defined $files[-1][1]) {
        close $files[-1][0];
        pop @files;
        next;
    }
    
    chomp $files[-1][1];
}

while (@files) {
    my $minRecIndex = 0;
    
    # Find the current minimum record
    for my $cmpRecIndex (0 .. $#files) {
        $minRecIndex = $cmpRecIndex
            if $files[$cmpRecIndex][1] < $files[$minRecIndex][1];
    }
    
    print "$files[$minRecIndex][1]\n";
    
    my $fh = $files[$minRecIndex][0];
    $files[$minRecIndex][1] = <$fh>;
    
    if (defined $files[$minRecIndex][1]) {
        chomp $files[$minRecIndex][1];
    } else {
        close $files[$minRecIndex][0];
        splice @files, $minRecIndex, 1;
    }
}
[download]

Prints:

1
2
3
4
7
10
11
20
22
24
29
30
90
[download]