There are methods for displaying and tying into vBulletin data on external pages. Much of it is documented on vBulletin.org, amongst others.
However, you may not be able to put it on an HTML page. It will be PHP code, meaning that you either:
- Make php pages, not html pages, -OR-
- Run html as php on the server. This can be done, but is often not suggested for various reasons.
A php page can hold pure HTML code.
As far as login-specific suggestions, I saw one at daniweb, although it fails to mention the version of vB and is from early 2008. See http://www.daniweb.com/forums/thread109707.html
As with anything else "crossover" in nature, you may just be in for a wild ride here, ending up with nothing functional after investing a lot of time in such a "hack". Just be warned.
Sometimes it's better to just include a link to the login page. For example, http://www.digitalFAQ.com/forum/login.php
and then be done with it