Is there any way to edit ODT documents on Android?
There is AndrOpen Office

AndrOpen Office is the world's first port of OpenOffice for Android.
You can view, edit, export office documents using full features of the OpenOffice.
AndrOpen Office has 6 components:

Writer (a word processor)
Calc (spreadsheet)
Impress (presentation graphics)
Draw (drawing)
Math (equation editor)
Base (database)

* AndrOpen Office is forked project from the Apache OpenOffice project.
AndrOpen Office is not affiliated with the Apache OpenOffice project.