The following has nothing to do with your Dish Network channels that arrive by DBS:
First, I am not aware of any SD Dish boxes EVER having analog demods; the old SD boxes did have ANALOG PASS-THROUGH allowing you to use your TV and its tuner to watch local channels in the days before the digital transition, especially when DBS was forbidden to provide local channels, except for the 5 Superstations via satellite.
Actually, the off-air Anaolog in the HDTV Setup menu refers to the built-in (or added module for the "K" series and 922) OTA/analog tuner and which analog band you wish to receive your local OTA or Cable channels, as digital OTA is still broadcast using ANALOG RF (just like Dish Network and DirecTV); it is the data being transmitted on this ANALOG radio frequency that is "digital" or HD and the same for "digital" cable.
1.Offair: means the tuner will demod the OTA band of frequencies to provide your local broadcasters digital and HD channels when connected to an antenna.
2.HRC or IRC: refer to different analog bands used by Cable TV systems. This feature was desinged to allow Dish subscribers to receive there local digital and local HD channels via a cable subscription to the NON-encrypted (open) bands that many cable TV systems still put the local OTA digital channels and viewing them through the Dish box.
While #1 is very popular with power users and works very well, #2 seems to not be active, nor am I sure it was ever active. #2 was designed in the early days of digital OTA when DBS offered ZERO local OTA digital via satellite. It was designed to get you locals so that you wouldn't feel the need to drop DBS and go back to cable.
However, that was YEARS ago, and today DBS offers all the most popular local OTA digital channels (major nets and a few more), so the use for #2 is somewhat anachronistic now that we can get those channels via satellite and certainly NOT involve the cable company providing any level of service to compete with Dish.
So, in summary, #1 can be of good use to you if you are interested in receiving MORE OTA digitals than what Dish offers on satellite, including all the multi-plex channels such as Universal Sports, This TV, ME TV, Antenna TV, Living Well in HD, etc., which are currently NOT available via satellite. #2 is pretty much useless these days, so you can forget about it.