YYou don't organize the photos in itunes. You organize them on your PC. One way to do this is to create a master Photos folder somewhere on your PC. In that folder create folders that will contain photos. Each folder will become an album on your iOS device. Do not create any sub folders in the album folders.
then connect your iOS device to your PC and run itunes on the PC. Select your device and select Photos from the row of tabs that are presented. Carefully reivew the choices. You should be provided with a choice to sync selected folders of photos. You'll need to navigate to your main photo folder to see all the albums you created. Select those albums you want on the iOS device and click on Sync or Apply.
Later, if you want to remove an album repeat the process but deselect the unwanted album. Then click on Apply.
If you want to delete an individual photo, before opening itunes move the photo out of the folder its in on your PC. Then run itunes, connect your device, and click on .sync. Photos no longer in their original folders will be deleted from the albums on your iOS device.