Is there a way to enter grades that are not assignments originally completed or turned in using Moodle?
You will want to create an "Item" in your gradebook, the same way you create a new category. Each item should be given a short name. You will have to administer a manual grade for this created item, since it is not connected to a Moodle activity.
To administer a manual grade, click on your gradebook link, turn editing on and boxes should appear. Make sure you only put manual grades in the items that have been manually created, or you will be setting a default system that will not let your automated activities place in grades when needed (aka, quizzes)