Now that I think of it, it can be greatly simplified:

sub prepare_sort {
    return [ $_, tr/aeiou/z/cr, tr/aeiou//dr ];
}
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Thanks to Zucan for the tip!

So we dont need a sub now:

#!/usr/bin/perl

use warnings;
use strict;
use feature qw{ say };

my @words = qw( xaxexix babebib xaxexi babebibb baebbib );

say for map $_->[0],
  sort { $a->[2] cmp $b->[2] } # vowels sort
  sort { $a->[1] cmp $b->[1] } # positional sort
  sort { $a->[0] cmp $b->[0] } # alphabetical sort
  map  [ $_, tr/aeiou/z/cr, tr/aeiou//dr ],
    @words;
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