Okay, you cannot connect *directly* to a theme file like that. There's your first mistake.
What we're trying to figure out is how yowant people to actually access these extra loops. Where are they going to be? How are you wanting to link to them?
You said I do not need to create these as WordPress pages., but in point of fact, yes, actually you do. Only WordPress pages can access WordPress data.
If these extra php files you made have Loops in them that explicitly use get_posts or WP_Query or whatever to get what posts they want and such, then you should be able to simply turn them into Page Templates and then create new Pages (which will be empty) which use those Page templates. Then they will be accessible as standard WordPress pages.
First read this:
Next, turn one of your php files into a Page Template by adding the appropriate header to it.
Then, create a new Page using Write->Page.
Select your template on the right.
Your Page will now be accessible at http://example.com/Pagename .
Is there a way to tell wordpress to treat these new multi-category template files like it treats index.php? -- connecting it to an address on the main site structure (i.e., http://okwueagle.com/campus-life.php) -- and allowing it to pull posts from multiple categories into various places in the same page?
See, you're confused about the way wordpress works. It doesn't magically turn links on the main site into links in the theme folder. The index.php on the main site *actually exists*. It loads the blog. In point of fact, it *always* loads the blog, regardless of what the URL is in the address bar. It uses URL rewriting, and the content of the address does not refer to the actual directory structure of the site in any way at all.
Forget the old ways you know about putting html in folders and building a folder structure to create different URLs. WordPress does not work that way.