I think it's a common problem with the WP (8.1) OneDrive app and cellular data. I myself started a thread here about it on 03-29-2015. And I also noticed another thread by akthelonelyman from 04-29-2015 asking about the same problem. Both threads are here in the Windows Central OneDrive forum. I can't yet post links, so I just give the description.
Generally what works for me is to use WiFi instead of cellular data. Then all OneDrive uploads and downloads work.
For pictures I can also use cellular data. But not through the OneDrive app. Instead, open "Photos" -> "Albums" -> "OneDrive" -> "OneDrive Albums" and navigate to the pictures you want to download to your phone there (I think on OneDrive the pictures have to be in the "Pictures" folder or subfolders of the "Pictures" folder for this to work). You can individually download pictures to your phone by opening a single picture and pressing the "save" button. As far as I can see there is no option in the photo app to select and download multiple pictures at once.
I am by the way using a virtual network (MVNO) where I have to turn on data roaming, i.e., national roaming, in order to use cellular data. I have not yet had the chance to check if that causes the problem, i.e., if cellular data OneDrive uploads/downloads would work on a non-roaming connection.