I'm continuing a project from someone else and even after I turn off all the layers, there are still labels displayed in the data frame. None of them have "label features" on, so I'm not sure where these labels are coming from. I'm using ArcMap 10.5.
Your labels probably aren't labels. They are annotation, stored in the map document. Check the answer here, for your likely solution:
Go to the Data Frame properties to view the Annotation Groups.