[Frankenstein]

I do not own a Droid device (desperately waiting for the release of OmniOutliner for iPad!), so I might not be able to help you, but you could export your outliner document as an OPML file. This is a standard file format that many other outliners can open. It is now up to you to find out if there is such an app for Droid that can open these files. Of course, this implies that you won't be able to open the original OmniOutliner files, and any changes you've made to the document on your Droid device will have to be re-imported into OmniOutliner, but I guess it's better than nothing.