Can a cell phone's IMEI be tracked even if it is switched off?
Off and "Off" are two different things. Off is battery removed. "Off" is standby, where the phone still has power, and allows it to respond to the power button and or usb cables being plugged in or docks.

If "off", it depends on how the phone was designed. If it was designed to still enable the cellular radio every n milliseconds to ping or talk to cell towers in the area, then yes, it can be tracked. Same thing with the microphone. If the phone has power, and the radio turns on, and it receives a secret message to enable the microphone, it can spy on you. Of course, that depends on if you believe those type of backdoors are real or not.