Climbing Hydrangea is very fast growing, lush green from early spring, but not evergreen. There are a couple of varieties with good scent.
Flowering Currants are good for rapid growth.
Clematis Montana, again for fast growth.
A lovely unusual fast growing tree is 'Katsura Japonica' or candy floss tree - Gives off a burnt sugar scent in the summer and can be easily trained to grow outwards rather than up (i have one and it is lovely - bought from ebay a few years ago)
You could plant a fast screener, then put a fragrant smaller shrub at the bottom for the scent?
Avoid Dogwood and chilean glory vines like the plague as they will take over and grow round next doors dogs if they stand still long enough :)