Dissolve yeast and 1 tsp. of the sugar in 2 1⁄4 cups lukewarm water in a small bowl and set aside until foamy, about 10 minutes. Grease a large bowl with 1 tsp. of the oil and set aside. Grease 2 large or 4 medium baking sheets with 2 tsp. of the oil and set aside.
Using a kitchen spoon, beat 4 of the eggs in another large bowl, then beat in salt and the remaining sugar and 1⁄2 cup oil. Add yeast mixture and beat until well combined. Gradually add flour, stirring until dough is stiff. Turn dough out onto a lightly floured surface and knead until smooth, about 15 minutes. Shape dough into a ball and transfer to prepared bowl. Cover with a damp kitchen towel or plastic wrap and set aside, in a warm spot, to let rise until doubled in bulk, 1–2 hours.
Preheat oven to 350º. Turn dough out onto a very lightly floured surface, divide into 12 equal pieces, and shape each into a ball. Set dough balls aside about 2" apart, cover with a damp kitchen towel or plastic wrap, and let rise for 10 minutes. Roll dough balls into 12"-long ropes.
To make the six-strand braided loaves, line up 6 of the ropes lengthwise on each large baking sheet, or, to make the three-strand braided loaves, line up 3 of the ropes lengthwise on each medium baking sheet. Position baking sheets perpendicular to you. Join ends of ropes at top of baking sheet and pinch together. Braid each loaf, join ends of rope at bottom of baking sheet, pinch together, and tuck ends under on both ends of loaves. Loosely cover loaves with damp kitchen towels or plastic wrap and let rise for 15 minutes.
Beat the remaining egg and 1 tsp.water together in a small bowl. Brush tops of loaves with some of the egg wash, sprinkle with poppy and sesame seeds (if using), then bake until loaves are deep brown and hollow sounding when tapped, 45-60 minutes. Set loaves aside on rack to cool.