the olivea shoudl work with jsut hdmi. Also, with hdmi hooked up, there is an option to force optimal resolution. See if you can find that. Make sure absolutely nothing is plugged into the weird jack where the AV component pack plugs in.
If you have the analog AV pack with toslink hooked up at the same time,, it won't matter what you do, HDMI won't work. the x360 AV connector over-rides HDMI, and scrambles the picture. I'm virtually certain that's what's going on.
so, no matter what, if you want toslink plus HDMI, you have to buy the new MS audio only av pack. that's your only option for hdmi plus toslink.
edit, my bad, i did not see this part.
These attempts were made w/ only HDMI, not using the AV pack simultaneously.
in that case, try what the other users suggested. Also, I know of some instances where you have to have your HDTV tuned to the HDMI input, then boot the x360. YOu might also try to get 480p working, then try to force optimal resolution (in the settings panel)also, another thought, you could try hooking your x360 via HDMI to another display (if you have one) and get it setup in 1080i/720p (better yet, force optimal), then go back to your HDTV and try HDMI. Also, you could try the same thing on your comp LCD if you have a dvi to hdmi adapter.
just throwing this out there, may not work because of the olivea may have improper "i forget what called setting" but it's essentially the device ID info.