And airplanes with IRS do not have a magnetic compass, flux gate or any such thing. (Apart from a basic standby compass, similar and not as accurate to that in a Cessna 152). The flight instruments are fed from the inertial attitude, the direction of magnetic north is calculated from the True North sensed by the inertials and adjusted for local variation using a data base loaded in the IRS program.
During the setup period, which varies with the latitude of the airplane, the IRS senses the rotation of the Earth and uses that to determine True North, as well as Latitude. It needs Longitude to be given to it, and if the information is different to that which it had when last shut down, it will reject the coordinates you have given it. But if you override with the wrong Longitude again, it will accept it, and so will be skewed for the whole flight, and give incorrect positions, groundspeeds, headings and so on.
The program will search for DME/VOR signals in flight to update the displayed position, and will use this information if available. If not, (remote areas) it will use the IRS position for navigation. The program knows the location and altitude of all nav stations, all airfields and later versions also know the terrain, in the entire world! If available, it will of course use GPS to display the position, since GPS is the most accurate. On approach, it will use the LOC signal as a priority for position.
Most airplanes have three IRS fitted, and they "triple mix" to obtain an average of these for position. If one or two fail, it still works, but is not as accurate. The failed IRS is still usually available for running the flight instruments (But if that is the case it is necessary to update the Heading frequently, just as you do in the Cessna with a giro heading display).
Great system, but better may be on its way.