What's THE correct pronunciation?
Given that few ancient Greek or Roman astronomers are around today to help us with correct pronunciation, I'm happy to report a little gem has surface, published in 1942 by Adler Planetarium, that might help settle matters. The pamphlet is called Report of a committee of the American Astronomical Society on Preferred Spellings and Pronunciations - see attached. Therein, the Latin genitive (possessive) for constellation Auriga = Aurigae and is marked "o - ri - jee" - as in the concatenation of ORIon and GEE, O-RI-GEE. However, unless you meet an ancient Greek or Roman, we'll probably know to what you refer, no matter your preferred pronunciation.