Something like:

while ($line = <ALBUMS>) {
    ($artist, $album, $song, $location) = split('\|', $line);
    $songlist{$artist}{$album} .= $song . "+";
}

foreach $artist (sort keys %songlist) {
    print "Artist: $artist\n";
    foreach $album (sort keys %{$songlist{$artist}}) {
        print "  Album: $album\n";
        print "    Songs:\n";
        $i = 0;
        @songs = split('\+', $songlist{$artist}{album});
        foreach $song (@songs) {
            $i++;
            print "    $i. $song\n";
        }
    }
}
[download]

(Though this code is untested)