All of my birds have traveled & have ridden in cars, trucks & my van. Some people find their birds get car sick, but that has never been the case with my guys, and a couple of them have been on a trip over 900 miles. Although I don't know for sure, but I mount the travel cage so that the bird(s) can see what is going on...not down in the seat & only see what goes by above.
While I don't take all at the same time, I've not had any problems with them.....just nosy animals where we might be visiting.....got to be careful of someone else's animals.
Also where you're visiting may use candles, air fresheners, teflon coated stoves, pans or other appliances, all potentially deadly to your little GCC.
As long as your car is in good working order, you shouldn't worry too much about traffic fumes.....unless you are driving in heavy traffic areas in China. Pre-heat the car & be prepared to carry your feathered friend inside your coat if you were to break down.