Is it possible to trace a mobile through its IMEI number provided that is not switch on or neither it have any sim card in it or without any phone tracker software
I think just if its off means there is nothing to with network signal or IMEI.
In any case if the mobile is on there might be some posibility.

Your airtime provider can remotely disable your device when it attempts to register on the network, but YOU cannot.
There are tracking packages available, but they need to be installed BEFORE you lose your device.

If the device is not switched on then there is NOTHING that can be done as it will not identify itself..