Turning Dropbox and OneDrive off is actually what keeps those files stuck. "Needs to be downloaded" means what's on your desktop is just a placeholder, the real file lives in one of those clouds, and only the app that put it there can bring it back. iCloud refusing to take over the Desktop points the same way: another app is already backing that folder up.
So start both apps again and right-click one of the stuck files. The app that's holding it adds its own items to that menu, and one of them usually downloads the file or keeps it on the Mac. Once it's downloaded it moves like any other file.
If it turns out to be OneDrive, its desktop backup is under the cloud icon in the menu bar > ⋯ > Preferences > Backup > Manage backup. If you stop it there, the files stay in OneDrive and a "Where are my files" shortcut appears on your desktop, so you can drag them back to the Mac from there.
— Dmitry · developer of ComfortFiles