WordPress coexisting with Omeka

I am currently setting up a WordPress website for a small museum. I have also set up an Omeka (very similar to WordPress) site to keep track of all the museums pieces and collections. I have developed A WordPress theme, and Omeka theme to both look as though they are one site, so the end user wont notice the switch.

What I am wondering is there any way to access WordPress features from within Omeka (outside of WordPress) such as continuing to use the WordPress Menu Bar on the Omeka Site. Possibly sharing headers and footers even? I’m also looking for ideas to integrate the other way, I.E. Omeka “Featured Items” in a slide show on WordPress for example.

Thanks!