iCloud is full but iphone storage is empty
There are two options for iCloud Photo Library: 'Optimize disk usage' and 'Downlaod and keep originals'. Optimize disk will delete original photos from your device and keep only thumbnails to free up space, while 'Download and keep originals' will keep originals in iCloud and on your device. 

From what I know there is no easy way to delete photos from iCloud. If possible, the best option will be extending the iCloud storage.

If not, you can try the following:


Go to Settings > Photos on your device and tap on 'Download and keep orogonals'.
Leave your device charging overnight with a strong Wi-Fi connection to make sure that all photos are loaded (there is no progress bar for downloading original photos).
Delete photos from iCloud to free up additional space.


Be aware that in this case you won't be able to use iCloud Photo Library as the storage will get full again. The only real optio is backing up photos to your computer (Image Capture on Mac or drag&amp;drop with Explorer on Win), then delete photos from both device and iCloud.

Hope this helps.