Most sdcards are formatted with a fat file system. you could take the card out and try to do a recovery on it but it looks like your stuff is just gone now. You may just want to reformat the sdcard and start over. You should always do a clean removal of usb and not just unplug it.

 

Assuming Nexus 5, there is no physical SD card to remove.
If the sdcard partition is corrupted, I suspect user apps won't be able to run either(?)

Have you rebooted since the problem started? (not sure if it will make things worse or if it will solve it)