Addressable low power radio
To answer your question:

"Are there Tx/Rx ICs I could use which power off until a signal is received"

No not really: receivers are "high power" devices. Even the lowest power receivers will use mAs as @pjc50 notes. 

The current work on low-power radios focuses on duty-ratioing and/or time sync techniques to save power and achieve long run-times with small batteries. The goal is to minimize the time the radio is on as much as possible but still have a responsive network.

Contiki and TinyOS are two embedded operating systems with this focus. They both run on a variety of low-power wireless microcontrollers and implement different low-power control schemes for radios. You could use any of the hardware supported by these OSes to complete your project. Both have sample code that should be easy to modify for your purpose.