What programming languages should I study to better understand Omeka? Eventually I would like to try to customize my instance and perhaps build my own plug-ins/recipes. I'm not sure where to start in terms of learning the appropriate things to help me use Omeka more effectively.
If you're just starting, basics of PHP will get you enough to start altering themes and making basic plugins. The documentation will help you see how to use more of what Omeka does.
Eventually, to understand more of the inner workings of Omeka, you'll also want to learn a bit about Zend Framework, which Omeka is built off of. The released versions of Omeka use ZF1.
You can also ask questions on the developer email list or in the IRC chat #omeka
Hope that helps.