With the Onkyo TX-SR805S as the centerpiece of your AV setup, all external components will plug into it and it will be the brain. It has 3 HDMI inputs, which means you will have an HDMI input for DVD (standard, HD or BluRay), one for cable/sat TV service, and one left over for gaming or whatever. All audio and video from those sources will flow through this one AV unit. What you get determines what capabilities you will be able to use.
In other words, if you decide to go with DirecTV (D*) for TV service, you have several receivers (IRD's) to choose from. If you go with a DVR, you will get dual tuner functionality, plus the ability to add an off-air antenna to the DVR so you can get local programming in HD (if not already available through D* where you live).
This particular AV unit does not appear to have a built-in ATSC tuner (based on the zoomed in image available through Crutchfield's website). But that does not mean that you TV doesn't. If you TV has an ATSC tuner and TOSLink/Digital Coax Out, you can route the audio from the TV up to the AV unit and play the sound through there.
This is just a quick answer to some of your questions, but might get you past the initial confusion.