By default, sort will DWIM into simply sorting numerically and alphabetically. The little anagram checkers put each individual letter of a word into an array, and then sort that array. Here's the same basic algorithm in a little easier-to-follow form:

my $check1 = 'OLDENBURG';
my $check2 = 'GRUBENDOL';
my @array1 = sort $check1 =~ /./g;
my @array2 = sort $check2 =~ /./g;
print @array1, "\n";
print @array2, "\n";

my $an1 = join '', @array1;
my $an2 = join '', @array2; 
print "Is anagram: ", ( $an1 eq $an2 ? "Yes" : "No" ), "\n";

__OUTPUT__
BDEGLNORU
BDEGLNORU
Is anagram: Yes
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I'd also like to claim the first Quicksilver refererence in the Monastery. (Just hope I don't have to delete this bit when somebody points out it's wrong :)