How feasible is it to track down source of number station radio signals ? How is it possible and how accurate is it to track down the origin of radio signals used by number stations that emit all around the world (and, as a bonus, how much does it cost approximately) ?
I'm thinking about cases where a russian spy living in the U.S. would listen at a regular interval to a broadcast sent from a russian station (located in russia). 
If it is possible, since when ? Was that already achievable during WWII ?
 A: RDF (radio direction finding) allows you to determine the direction from which a radio wave arrives at the receiving station. Assuming "most direct" propagation, that tells you the direction in which to find the source.
This is normally done by one of two methods. For example, when you are using the old ARVO syste to look for avalanche survivors (where each member of the party wears a LF transmitter), you have a directional antenna with a null (zero sensitivity) along a particular direction. You then finding the point of extinction - that is, you wave your receiver around until you get zero signal, and that points to the source. With multiple people approaching from different areas, you quickly find your buddy.
This method does not work well when the source is far away - because then you will want the strongest possible signal to improve the SNR of your measurement. In that case you will want a directional antenna with a large gain (and consequently a narrow angle of sensitivity). The effectiveness of this will depend on the wavelength - the larger the wavelength, the greater the size of the antenna needs to be (in the case of a circular aperature, it follows the same $\alpha=\frac{1.22\lambda}{d}$ resolution law as we know for optics).
The problem is that short wavelengths will bounce off the ionosphere in somewhat unpredictable ways (because the ionoshpere is not flat, and not always at constant height, depending on the time of day, solar activity etc)... so while you can detect the direction of arrival of short wavelengths with some (limited) angular accuracy, they may not come from the direction they appear.
All this is solved most readily by getting closer to the source - obviously, the angular resolution matters less when the distance to the transmitter is smaller; and as the signal gets stronger, you will be better able to determine the exact direction. An airborne system would allow you to get relatively close, and point more directly towards the source.
Incidentally - while a directional antenna may have limited angular resolution, you can improve the performance by looking "left and right" at the source: rather than aiming for the maximum signal, look how far you have to rotate the antenna to reduce the signal by 50%. Do this in all directions, and the "real" direction is in the middle of your points. This could of course be defeated by a transmitter that changes its transmit gain continuously over a wide range...
If you are pretty sure you have a direct line of sight, and you have well synchronized receivers, you can use the correlation between received signals to determine their relative time of arrival. This is the method that was used in the old DECCA and LORAN navigation system (in reverse... they had multiple phase-locked transmitters, and you as the receiver would know your position by measuring the difference in arrival time; but that solution can obviously be inverted). Those systems are pretty much obsolete now - their useful range was limited, and you needed maps with local correction factors to take account of additional path lengths due to mountain ranges, etc. Note- LORAN-A was experimental by the end of WW-2, so in principle such technologies existed in their infancy by that time.
