How can I transfer photos from my iPod touch to my new iPhone without iCloud

If the photos were synced to the iPod you have to sync them to the iPhone.

If they were taken by or saved to the iPod you can email and then save them to the iPhone's camera roll album

You can also import them from the iPod to your computer and sync them to your iPhone.

Synced photos are not included I the backup that either iCloud or iTunes makes.

If you restore the iPhone from a backup of the iPod photos in the camera roll will not restore since photos are not restored if you restore one kind of device fro another (e.g., iPhone form iPod backup)