In no particular order of preference
Akebia, the Chocolate vine fragrant purplish or reddish flowers, semi evergreen, pest and disease free, flowers have an edible pulp-any type of soil, tolerates shade. Downsides: plant two for fruit production, not a native North American plant, might be too vigorous if it likes it
Celastrus scandens, bittersweet, highly coloured red berries encased in yellow shells, tolerates shade, attracts birds, north american native plant, any soil. Downsides: berries are poisonous to humans, may be too vigorous with growth to 30 feet, best cultivars may be hard to find, need a male and female plant. Newest cultivar 'Bailumn' is self fertile (or a graft), larger berries or you may find a combo plant of 'Hercules' and 'Diana' the older cultivars
Humulus Lupulus, Hops, for the beer maker in your home!, vigorous, tolerates shade, interesting fruiting structures Downsides: not native, likely will die down to the ground
As I am bored with what everyone else has I am growing this plant from seed:
Kentucky wisteria, fragrant purplish flowers Downsides: probably needs more light, not interesting to birds, only available from seed where I live, see Gardens North
Whether a vine is evergreen is not always easy to determine as climatic factors play a part. A euonmyus plant is evergreen in zone 6 but not necessarily so in zone 5.
The wisteria and hops are the least likely to be evergreen in zone. The most likely is the Akebia. Look around for bittersweet vines in your local botanical garden or nursery for information on how they will behave for you.