Combine the water, sugar and yeast in a bowl to dissolve the yeast.
Using an electric mixer with the dough hook or mixing by hand, add the eggs, oil, flour and salt. Continue kneading until dough is soft and elastic, not sticky.
Place dough in a large greased bowl, turning over the dough to grease all sides. Cover with a towel and let rise in a warm place 1-2 hours or until doubled in size.
Remove from bowl, punch down and cut in half. Divide each piece into 3 pieces for braiding.
Cover and let rise in a warm place until the dough springs back lightly to the touch, about 1 hour. Heat the oven to 350F.
Brush the dough very gently with egg wash (you could sprinkle toppings like sesame seeds or poppyseeds).
Bake at 350F until the braids are dark golden brown and shiny, 20 to 30 minutes. Cool completely on a rack.