Do the HDMI ports support audio or do I need to go buy optical cables to use them on my STR-DG510

Get a 4 in 1 hdmi switcher.

cant use both hdmi and opti outs try sum setting in blue ray but u nee dto plug all blue ray dish directto samsung hdmi then 1 master digital out form tv to sterio digital i n ok tell samsung your output also

The HDMI on this receiver is for video pass through only. It basically only serves the same purpose as an extension cord for an HDMI cable that's too short.
For audio you need to connect either a digital coax, an optical or composite cables.

The Sony manual for this receiver is not wrong, it is just a little misleading.
It does in fact use HDMI but ONLY for the HIGH DEFINITION video portion of the signal, as output from the receiver to your television. High Definition Multimedia interface carries both audio and video, however, your receiver is not decoding the high definition AUDIO portion of it and passing it through the HDMI, nor is it passing any form of multichannel audio through HDMI. So you can see why the receiver is no longer available for sale from the Sony website. The HDMI connection on your receiver is redundant unless you are not using a multichannel audio format, in which case you would be using either the TV speakers or connect an additional audio cable from the TV's "audio out" back into the receiver for external speakers.
All that should be done is use the HDMI cable from your blu-ray player connected directly to your TV. That will give you your picture, and possibly a better one since the receiver will no longer be in the signal path.
Then connect either a coaxial or optical cable from the blu ray player to the receiver for your audio. You will then be able to have Dolby Digital and DTS surround formats.
Your service person was wrong.

For this Sony, you have to use separate audio cable(s). Either optical in BD or Digital Audio in DVD (single coaxial cable will do the trick) I bet the display says UNLOCK. I had the same problem, very dumb.

Good day!

You have to use the same connection in and out. You can not mix inputs and outputs (Example- HDMI IN will not play on Component out and Vice Versa.)

Make sure that these inputs are enabled. I'd have to confirm within the manual, but I believe that these have the HDMI section disabled by default.
Dan

I think you have to run a separate audio line from the dvd to the 510, because the HDMI is only passive

I called sony, even though the manuel shows that you can use a component wire to hook up the set top box and hdmi for the tv and dvd sony claims that you can not do this. The cable box must also be wired with an hdmi cable going into the video 2 port.sony claims it doesn't work using component and hdmi together because the receiver is unable to up convert. I hope this helps. I have not tried it yet (i'm at work) we'll see what happens when i get home.

What port do you have the HDMI from you BD player into on the 510. If you have it on the DVD port then fiber optic will do you no good, the DVD HDMI only supports digital coax, the Video2 HDMI only accepts fiber optic, and there is an extra fiber optic for the Sat input. If your BD player does not have digital coax out, or if you dont want to buy another cable, just move the HDMI from DVD to Video2 on the 510. I am willing to bet you have the BD player plugged into the DVD HDMI port and the fiber optic cable from you BD player to the Video2 fiber input.