According to the Etymology Online Dictionary odometer it comes from Greek hodos ''way'' + meter (from metron "measure").
Other words with these roots are: meter, telemeter and symmetry (with meter). Or electrode, diode and exodus (with hodos).

Classroom Blog of the Classical Civilization Students. IES María Casares, Oleiros, Galicia, Spain.
Greek and Latin Roots of English: Odometer
Greek and Latin Roots of English: Centrifuge
Greek and Latin Roots of English: Kleptomania
Greek and Latin Roots of English: Herbicide
Greek and Latin Roots of English: Genocide
Greek and Latin Roots of English: Hydrophobia
Greek and Latin Roots of English: Megalith
Greek and Latin Roots of English: Carnivore
Greek and Latin Roots of English: Cephalopod