In the Moodle gradebook you can move things around either one at a time and fine-tune their location in the process or you can grab a bunch of items at once and move ALL of them to the end of a selected gradebook category.
One or Many, Move to a Category
This is ideal for populating new gradebook categories with grade items in a faster method than one at a time.
Enter the Course you wish to rearrange the gradebook in.
Locate the Actions menu (gear icon), click the Gradebook Setup link.
Check the check-box in the right-most column of each item you wish to move into a given category.
Locate the Move select items to drop-down box at the bottom of the page and select the category you want those items placed in.
Confirm your changes are as expected.
Repeat as desired to populate or move the contents of your Gradebook categories.
Single, Fine-Tune Ordering
This is ideal for moving items into an expected order (assignment #1, assignment #2, etc.) or moving a single item elsewhere in the gradebook.
Many dashed boxes will appear between each item in the gradebook
Select the one between the items you want to relocate your selected item to.
Click on the double arrow icon 
to the right of the item you want to move.
Locate the Actions menu (gear icon), click the Gradebook Setup link.
Enter the Course you wish to rearrange the gradebook in.
Confirm your changes are what you intended.
Repeat as desired.