I have inherited down-and-feather-filled duvets and pillows which have not been used and have been stored for several years. Can I still use them?

Even if down and feather pillows and duvets are durable, they undergo a natural ageing process. While the down and feathers were stored they might have been exposed to damp or damaged.
 
You should have cleaned your pillows and duvets at the bedfeather cleaners´. They sift and clean the material there, pick out the filling components and replace them.
 
Quelle
Verband der Deutschen Daunen- und Federnindustrie e.V.