Hi, GrammerNazi,
Do I say two and one third years?
You should say "two years and four months." The point is that "half" can premodify "year" to mean "semester" (a half-year, half a year), while "third" cannot be used that way to mean "four months," unless you say "one-third of a year." The need to use "of a" prevents you from using "third" the same way as "half."
You can of course use "quarter" to mean "three months" (two and a quarter years, two years and a quarter), and in economic and other scientific reports you can use decimal points:
- 2.25 years = 2 years and 3 months, 2¼ years
- 2.5 years = two and a half years, 2½ years