Oh boy. Do I have a bone to pick with whatsapp. Their message data management is a complete clusterfuck.

Though if you just want to delete media, that’s easy. Whatsapp has it’s own folder in root that contains a folder for each file type. Edit: Not anymore, it’s in /Android/media/whatsapp/WhatsApp/Media now. You can safely delete them all, though media files will no longer be accessible in your message history, as WhatsApp has literally no way to keep that stuff around without monolithically saving all of it on your device, locally, forever.

Instagram saves content to a couple folders, all in easy to find places like root, Movies, DCIM and Pictures.

As for Instagram app data, you can clear that from app settings.