I have Android 2.3.4.
I have noticed that even When I turn off Wi-Fi, I still keep getting notifications, like - Gmail, Gtalk and Google+ notifications. If I open the said App then it says that it is not connected to internet.
So, my hypothesis is that maybe when I disable Wi-Fi, Android does not terminate currently established connections. It only denies new connections. But this does not explain why in this case the notifications are usually delayed, sometimes, by few hours or a full day.
What is happening and how do I actually disable the Wi-Fi?
PS: I use the "Status Switch" widget to turn/off the Wi-Fi.
UPDATE: the phone doesn't have a data plan, so data isn't coming in that way.