Receiving SMS by Arduino GSM Shield and control the LED with the content of this SMS?
First of all, you have a typo: You need the double-equals operator in

if (c == 'off') {


But more importantly, you can't use a char variable to hold or compare more than one character at a time. I don't know the details of the Arduino GSM library, but if sms.read() returns a string, then you'll need a string variable or an array of char to hold the result.