Unable to drop my infatuation with the Omni Group, I started a thread months ago in the Omni Forums pleading my case for OmniOutliner on my iPhone. While the Omni gang has been mum on this point, the thread has slowly grown with additional apostles. The most recent advocate, random1destiny, gave an excellent tip for viewing current OmniOutliner files on your iPhone.
For everyone else, until the OO iPhone app comes out, a good view-only solution I found is to buy the Files iphone app which lets you upload any type of file. Then export your OO file as HTML(Unordered List) and transfer and view it using Files. This results in a fairly readable copy that you can keep on your iPhone.
Why didn't I think of that?