I have an AT&T iPhone 3GS. If my phone is switched off and somebody sends me a text message, will they get a notification that delivery failed? What if they did not have delivery receipt turned on? Will they still get a bounce back failure message on their phone?

no the sender will not receive a delivery failed notification. the only time when the sender would receive a notification like that would be if they didn't have sufficient service to send a text out.

if they have delivery receipt turned on they won't receive a delivered notification until you turn your phone on and receive the text