It's confusing because Wordpress refers to "static pages" meaning Wordpress generated pages, but they are anything but static. For the purpose of discussion, when I say "static" it means an actual hard file, like index.html.
If the latter is the case, this is the exact same answer as the post here [webmasterworld.com]
with a twist. If Miva dynamically outputs pages via PHP, you can skip the bits about static HTML, just follow the parts about wp-load and query_posts.
If you want to drop **any** Wordpress element into a static page, you'll need to initiate a Wordpress instance. So The first thing you'd do is rename the main page index.php*.
Once you do that, you include wp-load:
<?php include ($_SERVER['DOCUMENT_ROOT'] . "/blog/wp-load.php"); ?>
Now, anywhere in your page, you can pull posts from anywhere - the example in the link above pulls the 5 latest posts from categories 6 and 12.
* If you're linking directly to index.html, you shouldn't be. Links to main should be just / or example.com/. So instead of jumping through hoops trying to keep the main page name index.html (like parsing HTML as PHP, or worrying about changing all your links, or something) add a mod_rewrite directive (or IIS equivalent) to permanently redirect any requests for /index.html to /. This will allow you to rename the main page as index.php without any problems.