Clips inside a playlist can be manually ordered to specify the sequence they appear on the web player or in an embed.
However due to the limited number of 15 clips shown on each page, you may not be able to reorder your clips across pages.
To be able to correctly reorder these clips across pages, you can manually change the number of clips shown on each page by tweaking the URL.
Simply add ?pagesize=50 to your URL to be able to see 50 clips on one page.
For example, if your playlist page URL was
https://omnystudio.com/p/test-show/playlists/3d68746d-45c9-4323-9a91-2123c6afc2a5
It should become
https://omnystudio.com/p/test-show/playlists/3d68746d-45c9-4323-9a91-2123c6afc2a5?pagesize=50
Now you should be able to see 50 clips per page and you should be able to reorder between pages.
Note: you can adjust the pagesize to even larger numbers however it may cause performance issues when loading the page