First of all, it's important to distinguish the difference in the referenced ages in the Twilight Saga. First of all, there is physical age. This is the age the vampire was when they were turned; the age they will look for the rest of their vampire life. As a vampire is frozen as they are upon transformation, they will remain looking their physical age, I.e. Rosalie was 18, Carlsisle 23, Emmet 20 and Alice 19. In Esme's case, she was 26 when turned into a vampire. Physically she is the oldest in the Olympic coven, although she is not the oldest - Carslisle is.
Secondly there is actual age. This is the actual age of the vampire, from birth to the current date. For example, Carlisle was born in the 16th century, thus making him more than 300 years old. Esme was born in the late 18th century, making her easily 90-100 years old. Edward is 100 years old, Rosalie, Emmet, Jasper and Alice are easily in their 80/90's