If disabling comments and requiring user registration does not prevent comments, something is broke.
Disabling comments and trackbacks does indeed prevent them from occurring, but for new posts only.
Comments and pingbacks can be enabled and disabled on a per-post basis. If you want them disabled, then you need to disable them on each post that you have them enabled for. The "Allow people to post comments on new articles" and the other setting on the Settings->Discussion page sets the defaults for new posts.
You can use the Bulk Editor if you want to change this for all your posts en masse. Go to the main Posts screen, and select the checkmarks beside the posts you wish to edit. In the dropdown at the top left, change the word "Bulk Actions" to "Edit" and click the Apply button. This brings up the Bulk Edit pane. Then, change the setting for the "Comments" and "Pings" both to "Do Not Allow" and click Update. All the checked posts will have comments and pings disabled on them.
This is a much more fine-grained level of control, and yes, it does indeed work properly. A post with comments and pings disabled cannot receive comments or pingbacks, of any kind. They simply get dropped.