All the functionality is contained in regular files, and included in the regular fashion. wp-includes/ and wp-admin/ hold the majority of the included files, and it's made up of both procedural format and classes. There's talk of moving everything to PHP 5 OOP within the next few versions which will result in a lot more of the functionality becoming classes, however most of the objects will still be wrapped with procedural 'shortcut' calls.

If you want to learn the process by which it loads the core, start in wp-blog-header.php and follow the path of includes (and requires).