Electronic – Low parts count and cheap radio modulation (hack)

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.

If I remember right, narrow band FM is used. "Narrow" refers to the small maximum frequency deviation from the carrier center frequency. In FM, more deviation means more signal to noise ratio. Less fidelity is required to send simple digitally encoded signals and voice weather reports than good quality music as commercial FM does. In this case, the deviation is 5 kHz (again, if I remember right).

As for how to build a receiver, that's no different than any other FM receiver. There are various topologies for that. At 160 MHz or so, you have to wake up and design such things carefully. It's not like 1 MHz AM where simple hacks can get reasonable results.