I’m running the latest versions of Audacity and OSX.
I hadn’t opened Audacity for a week or so, and now I can do absolutely NOTHING with it! I can’t update my preferences for mic and headset, and I can’t play or record a track. What the heck??? 
Let’s try this step by step…
You open Audacity - do you double-click the Audacity icon to get a new, empty project, or do you open an existing project?
Which menus and menu items are available?
When you say you can’t play or record, do you mean nothing happens when you click the Play button, or does the playback cursor move but you hear no sound?
When you say you can’t update your preferences for mic and headset, do you mean by going through Audacity (menu) > Preferences or by using the Device Toolbar?
Any else you notice that is different would be helpful in diagnosing your problem.
– Bill
the latest versions of Audacity and OSX.
We prefer actual numbers. You’d be shocked at the number of people running “the latest” three-year old software on “the newest” Mavericks.
I can’t update my preferences
You going to have to get closer than that. Preferences won’t open, or Preferences can’t find your headset (which isn’t that unusual)?
Did you recently upgrade to Yosemite?
If there are pieces of the system that just won’t let you in, you might consider repairing permissions.
Desktop > Go (upper left) > Utilities > Disk Utilities: select your system disk, and Verify Disk and Repair Permissions.
Koz