How do you get the message storage is full off?

Reset it by holding the power and home buttons at the same time until you see the Apple logo, then release.

Is your iPhone unresponsive so you are unable to use it?

Can you tell me the exact message?

That may be referring to the space on your phone, not the space in your iCloud account. Go to Settings>General>Usage. How much available storage does it show at the top?

Try going to Settings>iCloud>Storage & Backup, turn off iCloud Backup, connect your phone to your computer, go to the Summary tab of your iTunes sync settings, select This Computer under Automatically Back Up, click Apply at the bottom to sync your phone, re-select iCloud under Automatically Back Up, Click Apply at the bottom to sync again, check the size of Other in the Capacity Bar at the bottom, then disconnect your phone from your computer. Go to Settings>iCloud>Storage & Backup and confirm that iCloud Backup is turned on. If not, turn it on.

See if this stops the pop-ups. Also, how big was "Other" when you checked?

If it were mine, I would restore it. I've done this twice myself and Other dropped to around 1GB. It's likely that there is corrupt data on your phone that restoring should fix.

One thing you might want to do before restoring is to save you photo stream photos to your camera roll. To do this, open your my photo stream album, tap Edit, tap all the photos, tap Share, tap Save to Camera Roll. That way they will be backed up along with your other data when you back up your phone.

I don't know what else to suggest. At this point your options are to either contact iCloud support (http://www.apple.com/support/icloud/contact/), or make an appointment with the Genius bar at a nearby Apple Store to have it looked at.

Did you get this fixed? I have the same problem and now I can'tt download IO7 as it says not enough storage. I have 8.7 GB available.