I'm considering buying a 2006 Outlander with AWD. I occasionally go off-road in the desert. Does anyone have an idea how well the 2006 Outlander's AWD is suited for loose desert sands? Does it have limited slip differentials, traction control, or some other kind of locking that would prevent it from getting stuck in the sand?

On wikipedia you can read this:

...The four-wheel drive version uses normal ("open") differentials for the front and rear axles, with a viscous coupling unit for the center differential....

No, there is no traction control. Remember, it is more-less an road-use SUV with ability to enter easy-terrain roads. Definitelly not an offroader. For driving on non--pavement road it is great. But not for sand dunes....