I downloaded latest HoloEveryWhere
Then Import from existing code --> library folder --> Properties --> isLibrary --> Ok
Then Import from existing code --> Demo folder --> Properties --> addLibrary --> Library
And in demo i have i errors, see in images
Try removing the imports in the second image and then clean and rebuild.
import org.holoeverywhere.slidingmenu.R;
import org.holoeverywhere.slidingmenu.example;
import org.holoeverywehre.slidingmenu.SlidingMenu;
Also ensure that Inside the SlidingMenu library, that the class SlidingFragmentActivity extends SherlockFragmentActivity. Check the link below for more information on this. This is the only problem I could think of for the getSupportActionBar() without seeing the actual errors.
EDIT:
It may also be worth checking that your project is referencing the correct libraries. Right click on your example project in the package explorer -> Properties, then select android and check that in the library section that there are references to the SlidingMenu and ActionBarSherlock libraries.