Blend the strawberries with 2 cups of the sugar and 2 cups water in a blender.
To a large vessel, add the remaining 2 cups sugar and 5 1/2 quarts (22 cups) water and mix to dissolve the sugar. Add the lemon juice, lime juice, strawberry puree and cherries with their juice and mix; add more sugar if desired. Chill thoroughly.
To serve: Fill glasses with ice and top up with the strawberry-cherry lemon limeade.