Are my iPhone's photos deleted permanently?

Every time I plug my iPhone into a wall, it gives me a notification that says "Not Enough Storage
This iPhone can't be backed up becaue there's not enough iCloud storage available. You can manage your storage in settings."

Now I save a lot of photos to my phone, from the internet and such, and I deleted some photos that I did not want on my phone. I share this apple account with the music and stuff with several other people, but I have photo sharing off. I also never plug my phone into my computer to be synced with my iTunes. Since my phone is telling me that it's not backed up, are the photos that I deleted gone forever? I'm not saying this because I want to restore them, and I have no interest in my phone being backed up.

Added (1). I have photo stream off and have had it off for a while

It depends.
If you have photo stream, they'll still be there and you'll have to go delete them out of them. Just go to your photos and look at the bottom of the screen and tap on photo stream.

If you have iCloud it saves every photo even if you delete it from photo. But if you have no backup you should put pictures into the computer and save them there so anything you want to restore you have them save already. But yes you need to delete more pics or delete others stuff you have In backup