The mass of cables can be daunting, but remember that each cable has one, and only one function. The "signal" has to flow from one device into another. You have to rely on the labels where the connections are made and sometimes the colors of the wires to detect the connections.
Unfortunately, there are many ways to connect these devices. Engineers are always developing better ways to do the same thing, and manufacturers want to embrace both the new technology and provide for backward compatibility. As a result, you get confusion.
You should have a manual for the device. If not, you can download them online:
TV:
Sony eSupport - KP-51WS520 - Manuals / Specs / Warranty or
http://www.docs.sony.com/release/KP57WS520.pdf
Receiver:
Sony eSupport - STR-DG710 - Model Home (get the "hookup recommendation guide")
Video Recorder:
http://service.us.panasonic.com/OPERMANPDF/DMRE75V.PDF
I couldn't find a manual for the Direct TV receiver. Here's their forum for connecting the Direct TV receiver.
Discussion Forum
There are several ways to connect these devices together, and sometimes you have to make decisions as to exactly how to connect them together with the connections that are available.
On the back of your Direct TV receiver, there may be an "S-Video" connection (S-Video connector), an HDMI connection (HDMI connector), probably a Video connection (single RCA connector) , and a High Def video connection (3 RCA connectors). This is where you start.
RCA connectors:
RCA connector - Wikipedia, the free encyclopedia
HDMI connectors:
HDMI - Wikipedia, the free encyclopedia
S-Video connectors:
S-Video - Wikipedia, the free encyclopedia
There are two signals involved: Audio and Video. In some connections, both the audio and video are carried in the same cable and in other cases, you use separate cables (have to make it more difficult, don't we).
The steps involved are 1) Make a decision about how to move the signals from the Direct TV box to the Panasonic recorder. 2) Make a decision about how to move the signals from the Panasonic Recorder into the Television. 3) Make a decision about how to move the signal from the TV to the Multi-Channel AV receiver. I don't think you'll be moving signals from the AV receiver to the TV, though that may be possible.
Start by examining, with the help of the manuals, how it's connected now. Draw a diagram of how you think the signals are flowing (use arrows). Then figure out to insert the recorder.
Here's some specifics about the recorder:
In the manual, on page 9, they show how to connect the device when you have a VCR. Pretend that the Direct TV box is the VCR. Then you have an idea of how it will be connected. Page 10 shows you the actual connections.
The recorder is not a new design. There is no HDMI connection, for example. There are a set of "Component Video In" (three RCA jacks that can take HD video from the Direct TV box into the recorder), a Video In connector (paired with the audio in), an S-Video In, and an RF in (RF -- radio frequency -- is the same as a modulated TV signal that comes from off the air). You don't have to connect all of these. Only one is required.
This is probably as specific as I can get right now. If you have any more questions, please ask.