The easiest way to do this is using the query itself. You may specify a custom field name and then use that field to order the results:
[mashup query="post_type=any&meta_key=myfield&orderby=meta_value&order=asc"]
Note that only one field is supported.
The documentation for WordPress ‘wp_query’ has more details – different ordering types, changing the order (ascending/descending) or sorting by numbers instead of characters: