Beat together eggs, water, salt & oil. Stir in enough flour to make a stiff dough. Turn onto floured board & roll thin as possible. With sharp knife (or Joel likes to use the pizza roller) cut into ½ inch wide strips. Cover with cloth & let dry if you want to store or freeze for use later. I just let mine set long enough to handle easily, then drop into hot chicken broth and cook until tender.
I sometimes add & cup milk and 1 teaspoon naking powder to make sort of a noodle/dumpling combination. It will take about ½ cup more flour, but these will not be quite so "eggy".
Experiment to suit your own taste (don't expect the whole family to agree on them -- mine never did). Mike always wants dumplings, not noodles. Wayne just wants his chicken fried.