Where can I store common cross-site text (e.g. headings, titles etc.)

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You should build a theme settings page for all the “global” settings like social media url:s, phone number etc..

It could be something like this:
enter image description here

Here is a guide how to make a Settings page:

How to build a theme options page.

Or you can make a settings page with the new Customizer that comes with WordPress 3.4 so you can see your updates before you save it:

Look at this video to see what i mean:
http://www.youtube.com/watch?v=vD8v6u3noPg&feature=player_embedded

And here is how you can do it:
http://ottopress.com/2012/how-to-leverage-the-theme-customizer-in-your-own-themes/