Is there any benefit to having my website pass as XHTML 1.0 Strict vs. HTML 4.0 Traditional or any other doc type? I'd assume this would not benefit SEO in any way. Would that be correct?

Thanks in advance!

Yes that would be correct!

Benefits?
It's like pi$$ing oneself whilst wearing dark trousers. You get a warm feeling and nobody else notices!

Bragging rights and vanity is the real reason. Only you really care about it, and if you are conciencious about your coding, a "badge" on the site won't make any difference to you.
Valid "badges" on a CMS driven site with your name on it ain't going to impress anybody, once the end user has pasted a bunch of code from MS Word or Publisher in the page.

Sure! It's handy to make sure there are no glaring errors in the code, but it does NOT mean it will render correctly.
You could write absolutely perfect validating code, and it will still "break" in browsers.

Its a little important for SEO. But no one exactly knows it. But be sure if it is one of the factors for search engines to rank websites, It has a very little value for ranking results.

SOOOOOO

Are you saying that Googles "home page" shouldn't be #1 when searching for "google"??????