It seems that in some states nandina is considered invasive because birds eat the berries and disburse them - everywhere. But it’s not considered invasive in Oregon. Other information says that birds won’t eat nandina berries, anyway.
Carl Grimm and the folks over at Metro suggest that even if it isn't a particular favorite of the birds, it is a great landscape plant because of its hardy nature and water sparce ways. And it's not on any Oregon "problem plant" list.
Meanwhile, I'll also suggest pyracantha (fire thorn) . My mom had a fire thorn that always looked great against the brick front of the house with the dark leaves in summer and red berries in winter. And these days there are many types to choose from.
You can find brilliant, vigorous Mojave, the tiny (2 ft by 2 ft) Red Elf, and many in-between. The berries can be fire-engine red, a more orange-red, or really-orange. There's even a ground cover type called Low Boy. A variety to suit every bird lover's landscape.
Other shrubs offering red berries to the birds are kinnikinnick, red elderberry, some of the barberries, and the native red currant.
Photo thanks to Monrovia. Credit: Doreen Wynja