You can combine many sorts. Here's something quick and dirty: 
#!/usr/bin/perl

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

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

sub prepare_sort {
    my ( $vowels, $positions ) = ( '', '' );

    while (/([aeiou])/g) {
        $vowels .= $1;
        $positions .= sprintf '%03d', pos;
    }

    return [ $_, $positions, $vowels ];
}

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 prepare_sort(), @words;

[download]
Output: 
baebibb
babebib
babebibb
xaxexi
xaxexix

[download]

In reply to Re^3: Sorting Strings By Vowel Sequence by Anonymous Monk
in thread Sorting Strings By Vowel Sequence by NewToPerl777

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.