I used to wear my glasses over the helmet-straps for two reasons; a). My old helmet was a "LAS", and the straps were flush against my head (either side of the ears. b). The el-cheapo sunglasses I had then would "dig-in" above my ears & cause considerable irritation on long rides.
Now however, I wear a "MET" helmet, that has a slight gap in the straps between the helmet & skin around my ears. And my current el-cheapo sunnies are more comfortable. Hence, I currently ride with the eyewear under the helmet straps.
I suppose it depends on the brand of helmet & sunglasses, and then a bit of trial & error in finding the right combination. Another problem that may occur is eyewear-wobble. Some combinations affect how securely the glasses fit when going over bumps etc. The only suggestion I could make is to take your helmet into the glasses shop and try them on together.