If you want to make folders, the simplest way is to connect the device to a computer via USB cord. Then move all the files over to an empty folder on the computer. This will mean there will be none on the device while you are doing this. They will all be on the computer.
Create all the folders you want, and name them as you wish, on the computer. Then put the images into the folders you wish them all to be in. You can also rename the images to whatever you wish.
Once you are done sorting it all, you can then, via the same USB cord connection, copy the folders and their contents back over to the phone, or to its SD card. Which ever you prefer. I say copy because it is smart to leave a backup on the computer so you don't lose the...