Put 4 cups water and the sugar in a medium saucepan. Add the ginger slices, allspice and cinnamon. Heat until boiling and the sugar has dissolved. Remove from the heat, stir in the tea bags, cover and let steep for 15 minutes.
Strain the tea into a large pitcher, discarding the solids. Chill until ready to serve. (This can be prepared up to 2 days in advance and stored, covered, in the refrigerator.)
Just before serving, stir in 4 cups cold water and the lime juice and orange juice. Serve over ice and garnish with orange and lime slices.