The Omni Group does not have an API but they were kind enough to show me some documentation on their webdav/xml based sync format.
The current feature set is rather limited but it's enough to allow 2 way syncing. I plan to add some more features (notes and attachments) in the coming weeks.
This also makes me happy that they're willing to talk with developers about their sync format. That tells me an ambitious dev could create clients for Windows, Windows Phone, Linux, etc. as well.