My iphone has been stolen, I cannot remotly erase it because they have turned the phone off.

The phone needs to be turned on and connected to the internet in order to receive a signal to erase or to send a location signal. You have already found the link in blue above your name on this page. Read it carefully.

Nordyuob wrote:

Shall I delete from my devices then? Or do I wait for the thief to turn it on in the hope that he/she does and then the information is erased?

If and when the iPhone is erased, the erasure will remove it from “My Devices”.

You erase it as described in step 5 of the article linked above. The erase will occur once the iPhone is online.

Simple answer, you cannot. If your iPhone has been turned off there’s nothing you can do.