On my Verizon 4S running the last version of iOS 5:
There's an option for iMessage to send all iMessages as SMS, so it doesn't even worry about having a data connection. I've disabled celluar data on my 4S at times or had insufficent signal for a data connection, yet iMessage still sent messages as plain SMS.
The wifi radio does turn off when the phone's screen turns off (after a bit). I suppose because the WiFi radio used more power in standby during Apple's testing than their cellular radio, or maybe their cellular radio had better sleep states than their wifi radio choice. But that's just a random hypothesis. Regardless, I can't say I had any cellular data use with the cellular data option turned off.
Unless you're running iOS 6 and something has changed, or something is just messed up with your iOS install/apps, you shouldn't be using any cellular data with the option turned off.
There was a hubub a while back about early versions of iOS5 (I think) erronously sending diagnostics data over cellular connections, resulting in large data use. But I haven't heard anything about that for some time.
As the phone appears to be acting abnormally, try a factory reset. If it still seems to be acting odd, contact Apple or Verizon. Also, use the option to reset the cellular use data counter on the iPhone at the start of a billing cycle (or at the trigger of a new billing day, just for ease of measurement), and then after a few days compare it to what Verizon says your data use should be. If your phone is reporting significantly lower than Verizon's counter, something is certainly off.