The online eBook conversion service ODT2Epub announced an update recently where it streamlined the process, smoothed out more bugs, and generally improved the user experience.
This service has both free and paid options, with prices ranging from 19 to 89 euros. The free tier is ad-supported, while the paid tiers include file validation, extra users, advanced options for tweaking input, and a data log of past conversions.
On a related note, converting from ODT to Epub is one of the simpler conversion processes. ODT is actually rather similar to Epub; both are ZIP folders containing a collection of files and they share a similar organization inside the ZIP folder. In a pinch, you could rename an ODT file to Epub and it would be partially functional as an eBook.