In medium bowl, mix flour and salt. Make a well in center of flour mixture. Add eggs, water and oil to well; mix thoroughly. (If dough is too dry, mix in enough water to make dough easy to handle. If dough is too sticky, gradually add flour when kneading.)
Gather dough into a ball. On lightly floured surface, knead 5 to 10 minutes or until smooth and springy. Cover with plastic wrap or foil. Let stand 15 minutes.
Divide dough into 4 equal parts. On lightly floured surface, roll one-fourth of dough at a time into rectangle, 1/16 to 1/8 inch thick (keep remaining dough covered). Loosely fold rectangle lengthwise into thirds. Cut crosswise into 2-inch strips for lasagna, 1/4-inch strips for fettuccine or 1/8-inch strips for linguine. Unfold and gently shake out strips. Hang pasta on pasta drying rack or arrange in single layer on lightly floured towels; let stand 30 minutes or until dry. (If using pasta machine, pass dough through machine until 1/16 inch thick.)
In 6- to 8-quart saucepan, heat 4 quarts water (salted if desired) to boiling; add pasta. Boil uncovered 2 to 5 minutes, stirring occasionally, until firm but tender. Begin testing for doneness when pasta rises to surface of water. Drain pasta.