Sync all Photo Stream photos on iPhone
From Apple's Photo Stream FAQ:

How long are My Photo Stream photos stored in iCloud?
The photos you upload to My Photo Stream are stored in iCloud for 30 days to give your devices plenty of time to connect and download them.
How many photos are stored in My Photo Stream on my devices and computers?
iCloud pushes all your photos to the My Photo Stream album on your devices and computers, and manages them efficiently, so you don’t run out of storage space.
Your iOS devices keep a rolling collection of your last 1000 photos in the My Photo Stream album. From there, you can browse your recent photos or move the ones you like to your Camera Roll or another album to keep them on your device forever.

So, you'll have to sync them in from iPhoto using iTunes, since Apple only keeps your photos for 30 days on their servers.
You could also find another app on the App Store like Documents by Readdle and copy the photos onto your phone over Wi-Fi (bypassing iTunes as you wanted) but I realize that's less than ideal.