You can import your photos to your computer, if you have one.
You do not indicate that you are locked out of your phone. So, if you are not, then to import you would:
PHOTO IMPORT IOS TO MAC/PC
But, do you have your device signed into iCloud with Find My iPhone turned on? Because if you do, then you are going to need to take the device with your original sales receipt for that device, and a photo ID to your nearest Apple Store to have the Activation Lock removed. Since you cannot sign into your old Apple ID, you have no way to turn it off.
To turn it off yourself, you would need to know the passcode to the Apple ID. And trying to erase the device would land you in the same place, with a request to enter the passcode to that Apple ID to turn off Find My iPhone.
So, I would recommend that you Import your photos to a computer, if you can, then take the device to Apple with the documentation indicated above, and have the Activation Lock removed, then Erase the device so you can set it up as a new device with your new Apple ID.
Once you have done that, you will be able to sync back any of the photos you want to have on your device by syncing via iTunes: Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support
Best of luck,
GB