Put the water and oil in a pot. Leave them to reach boiling point, then add the flour while stirring nonstop. You're going to get a thick mixture. Remove from the stove.
After cooling, add the eggs 1 by 1, stirring after each. The mixture becomes thick and sticky. Use a spoon to place the dough for the eclairs into an oiled or covered with baking paper tray.
You don't need to shape them into anything in particular because during baking the eclairs will take on their shape. Bake them in a preheated 392°F (200 °C) oven about 25-30 min.
For the cream, dilute the flour in a little water and strain it so there's no lumps. Put the milk with sugar on the stove and after reaching boiling point, pour in the flour mixture in a thin trickle. Add the butter.
Stir carefully to prevent it from burning and to obtain a smooth cream. Remove from the stove and add the vanillas.
Cut the somewhat cooled eclairs down the middle and fill them with the cream using a small spoon. There's no danger of the cream spilling because the eclairs will stick back together.