Q: Why can I not recurve messages from other people without iPhones when my cellular data is turned off?

That is because regular SMS text messsages require cellular data, just like makeing and receiving phone calls, require cellular data.

Badceed wrote:

 

That is because regular SMS text messsages require cellular data, just like makeing and receiving phone calls, require cellular data.

That is not correct. SMS do not use cellular data, it's piggyback on the phone line.

Read this:

http://support.apple.com/kb/HT4146

Yes, SMS do not use cellular data, it needs a text plan provision by your carrier.

What did your carrier says when ask if your SMS is provision properly?