Need some help with Onkyo Ht-R, PS3 and Samsung 720p

I guess you're using an antenna for tv, instead of cable or satellite? How do you have the tv's audio going to the receiver?

It doesn't have to be Dolby Digital, to get all the speakers to work. You can set the receiver to Dolby ProLogic II (simulated surround), for tv, and all speakers should work. Otherwise, it should be set to "Auto". Then, when dvd is played, it will automatically go to the Dolby Digital 5.1 soundtrack. Same with HD channels on tv, if they are broadcasting in 5.1 surround.

There should be an optical output on the ps3, to go to the receiver. I'm not familiar with the ps3, so you'll need to look in the owner's manual, to see what audio output setting to use for optical. If the receiver has an optical input labeled "DVD", use that one. Otherwise, you may have to assign the input you use, to be the DVD input. Your receiver's manual will tell you how.

Do all the speakers work when you run the "test" cycle?
The speakers should be calibrated, so the volume of each speaker is the same, at your sitting position. To do it right, you need an SPL (sound pressure level) meter, and calibration disc. Amazon.com sells the Avia disc, and Radio Shack sells the SPL meter.

You should go from the DirecTv box to the receiver first, with video and especially audio. Going through the receiver with the video will make it much easier switching sources. So, you'll need another set of component cables to go from receiver to the tv. You can go straight to tv with component cables from sat box, but don't forget to change the input of the tv, to whatever input you use for the sat box, to watch tv. The tv isn't meant to pass the audio out to the receiver, unless you're using the built-in tuner, and an antenna. It won't daisy chain and get surround sound.

The DirecTv box should have either a digital coax or optical output, for audio. Digital coax output will be an RCA type connection, that's color coded orange or black. Also, go into the sat box setup menus, and make sure the audio output is set to "Dolby Digital".

For the ps3, if it has component outputs, I'd use them, going to the receiver first (since the tv is just 720p). Again, makes for easier switching. Then use the optical output for the audio, to the receiver. If you go from ps3 to tv with video, remember to change the input on the tv, to whichever input you used.

Most people use 12 AWG or 14 AWG wire for the speakers. 16 AWG is ok, but heavier wire is better, especially on longer runs (12 is heaviest of the 3).

Set up this way, Pro Logic II should come from all the speakers (for tv), but rear speakers are used less than the front three. They aren't constantly used. They're more for ambient noises. Most movies played on ps3 will be in 5.1/6.1 surround. Only very old dvds may not be 5.1 surround.

In receiver's setup menus, make sure all speakers are enabled. Set the distances (delay) from each speaker too. If you have all this set right, and you don't get sound from all speakers, something is wrong.

Yes.
Optical, digital coax, and HDMI, are the only way to get real 5.1 surround, except for 5.1/7.1 multi-channel analog outputs. But the ps3 doesn't have the multi-channel analog outputs.
Of course, you still need the HDMI or component for the video...............

If the box has an optical or digital coax output, there's got to be a setting for digital audio output somewhere. Maybe it just says "Digital" instead of Dolby Digital? If there's no optical or digital coax output, then you'll just have to use the red & white analog outputs, from the sat box to the receiver, and settle for Pro Logic from tv, even on channels you could normally get 5.1 surround. If that's the case, you might want to upgrade your service from DirecTv. If you already get HD from DirecTv, it's has an optical or digital coax output, so the setting is there somewhere.

It may already be set on the right setting, and the setting on the receiver may not be right. Going from the sat box to the receiver, the receiver will need to be set for DBS or SAT, instead of TV. The optical or coax input on receiver, you use for sat box, may need to be assigned to DBS or SAT also. The receiver's manual will tell you how to assign inputs.

The component cables you have running from sat box to tv are for video only. It's ok to go straight to tv, but you must remember to change the input on tv, each time you go from dvd to tv, and vice versa, since you're using HDMI from ps3. Since your tv isn't 1080p anyway, I'd use component cables from ps3 also. Then run component cables from sat box and ps3 to receiver first, then component cables from receiver to tv. That way, you want have to change the input on tv, everytime you switch from dvd to tv and vice versa. Is this getting confusing yet? Sorry!

If someone else can come explain this any simpler, you're welcome to do it. It's even getting confusing to me now, and this stuff usually doesn't confuse me very much.
It's a matter of understanding how inputs and outputs work together, and what settings to use with what. The hardest part, I think, is learning about assigning inputs, to what you plug into it. And manuals are usually pretty good about walking you through it.