OK I emailed myself a file saved in .odt format and when I attempted to open it I was prompted to search the store for an app. One application is Office+, which is a paid program ($.99) with a free-trial. Go ahead and look that one up in the store and see if it works for you. It looks like the last update to this was back in July 2013.
Yes, you can open an .odt (as well as some more exotic formats like .hwp) in ScanWritr app. You can also change it to PDF, annotate, add signature, mail it, fax it, save to the cloud etc.