My omeka site has a strict standards error at the top of the page: http://dlib.info/omeka/chromebicycle/
As a quick-fix I tried simply deactivating Image Annotation, but that resulted in individual items receiving an error.
Unfortunately I no longer have access to the phpmyadmin account that was used for the initial site set-up. I'd really just like that notice to go away.
Should I instead un-install Image Annotation?
You're running on a significantly out-of-date version of Omeka and a plugin that's just as out of date, so support is a little tricky.
If you're not using Image Annotation, deactivating it or uninstalling it is the way to go. The error you're getting when you deactivate it would happen just the same if you uninstalled it, though. That error's probably happening because you edited your theme to include a call to show the Image Annotation interface in items/show.php. Removing that call should prevent the errors you were getting when you deactivated the plugin.
Otherwise, if you are using Image Annotation and want to keep doing so, there's a couple quick-and-dirty options for getting rid of that Strict Standards message.