Since the Elemental Chaos separates the Astral and Ethereal Planes, spells and abilities similar to Etherealness wouldn't have any effect while in the Outer Planes. - PHB, pg 303
You could use Etherealness while in the Elemental Chaos or any of the Elemental Planes however, since they are considered to be adjacent to the Ethereal Plane, just on the other side of it compared to the Inner Planes. You would be in a region of the Border Ethereal closer to the Elemental though and so you may have to worry about adverse conditions while there (consult your GM for guidance on this.)
If you find yourself in the Outer Planes and in need of an effect similar to Etherealness, you should consider using Astral Projection instead. This could potentially allow your character to slip into the Astral Plane in a similar way to how someone would slip into the Ethereal Plane from the Inner Planes, although with certain limitations, such as leaving your physical form behind, rather than transferring it with you. - PHB pg. 215
You could consult your GM about possible items such as the "Oil of Astralness", which in theory would act in a similar fashion to the "Oil of Etherealness", but such an item would likely be considered a homebrew by the GM, despite its relatively minor alteration in the functionality of the original item. It may be that exposing your mortal form to the raw power of the Astral Plane might have potentially harmful side effects, or in some way limit the functionality of the item being used.
Or it may transform your character into a deity.