The "paid assets" clause refers to your source submission. Basically, nothing in your source submission can be a paid asset. However, you are free to use paid tools during the jam. It would be insane for us to say you can't use "Photoshop" in this jam because it is a paid asset, or say "World Creator with the Unity bridge importer tool" because that is a paid asset that hooks into a game engine for the export.
To answer your question directly, you may use Odin Inspector during your development, but you need to remove the asset from your source submission. I'm a fan of Odin personally and know how useful it can be during development and debugging, so it would sadden me if I couldn't use it myself :)