[Zubersoft]

As McAroni suggested, the simplest approach is to go to the Collections tab, tap the collection containing the songs you want to move, long press to start selection, tap the select all icon at the bottom right, then tap "Edit Songs" to perform a batch edit. On the batch edit screen, remove the collection and then add a Genre with the same name. Tap OK to save the change. You can then delete the collection if you no longer want it. You can use this same approach with Artist and Composer. Note that you can delete an entry in the batch edit screen by long pressing on the entry and selecting "Delete". So this may save you time if you want to first delete the existing collection or artist, then enter the genre or composer and save.

Mike