ODF support on phones and tablets is not good right now. Work is being done to improve this by the Calligra project, but WebODF can provide a solution too. To prove this, I built a small wrapper application that gives Android the ability to read ODF files. This application is available in the WebODF repository and I've also put the installable application online.
To reach more phones and tablets, such as the iPhones, iPad, Blackberry and Symbian phones, we could use PhoneGap. Making a PhoneGap application from WebODF code is a nice way to get started on cross-device development and to help out with the adoption of ODF. If you want to give this a try, check out the WebODF code, get PhoneGap, read the code for the Android example to see how to adapt the WebODF runtime and get hacking. Good luck and have fun!