The bird system is simply a delay line. As the conduction speed of signals in nerves is low, much lower than the speed of electric signals in cables, a series of coincidence detectors as illustrated in the figure can code for interaural delay. The neurons in the delay line will only fire if a signal arrives at the same time from both ears, an by making the nerve fibre from one ear longer than the finbre from the other ear, the cell will fire at a preferred delay. Each coincidence detecting neuron has its own tuning curve (sinusoidal curves in b) and so cover the entire range of interaural delays.
In mammals, all delay-sensitive neurons are tuned with maximum sensitivity to delays outside the maximal possible delay between the ears and the interaural delay is thus directly coded in the level of response (straight part of curve in the purple part of the figure in d).
Coincidentally, the leading expert on this (and author of the paper) Benedict Grothe, happens to sit right across town from you!