I'm bit out of date on this (I've done online media kits but not in the social media age), but you would probably be well-served to start with the following:
* The show's press release
* Several photographs of the actors in the current play in rehearsal. Make sure the actors don't have their scripts in hand (apparently this is a no-no), and be sure to include slug lines with each photo that are interesting, informative and have each actor's name included as they appear in the photo.
* Copies of the show's poster/flyer/e-blast, or other promotional material
* Information on the theatre company's season, history and creative mandate, as appropriate
* Information on the theatre itself, especially if it is of any historical or cultural importance
* Summaries of the creative bios of the director, major actors and other key players (musical director/choreographer, etc)
* Information on any production sponsors (check with your producer for any specific rules on this regarding placement, copy, graphic standards, etc)
Obviously all documents should be hyper-linked to further information wherever possible, but a lot of publications will just run your stuff verbatim, so it should all be ready for the public "as is."
In terms of social media, again this isn't my area of expertise, but a Facebook presence is a must, as is a Twitter feed. Pinterest and Instagram are growing in importance, at least for the next few seconds, and possibly FourSquare, depending on your location.
In terms of resources check out Seth Godin's blog, maybe, and the "Punk Marketing" guys - I think they may have some information that you will find helpful.