How do I mount 20 lb speakers to drywall between studs?
They make many different types of wall anchors.  I have used different forms of E-Z Anchors for years and am happy with them.  They hold up to 100 pounds in sheetrock with their toggle lock anchors.  1 of the normal screw anchors can hold 25 pounds in half inch rock.

I am sure those brackets have more than one mounting hole?  Place on the wall where you want, mark the holes with a pencil, "screw" in the anchors in the pencil marks and attach with screws and you should be good to go.  Now, this is assuming there isn't 1/4 inch rock on the walls :-)