While the TV will likely output audio over optical, it will almost certainly be limited to stereo. Some TVs will output DD 5.1 from external devices. But, very few do DTS and the vast majority of BDs have DTS soundtracks. So, you need to run optical or coax direct from the devices to the receiver in order to get discrete 5.1.
Your TV will output audio from our PC but it is always going to be Stereo unless your TV supports 5.1 out ( and most dont ! ).
Does your PC have a 5.1 analog output ? If you have this ( meaning three 3.5mm jacks, or a SPDIF Port ( looks just like your 3.5mm port - Check manual ) ) you can connect it to multichannel input in your receiver and you will have 5.1 ( just set your windows preferred sound to this source.
Yes, your computer will send audio and video signals to your tv via hdmi. that will work again, but again may not be 5.1 PCM or DTS.
You may get awesome video with the HDMI but not sound as you are trying to route it throught the TV. You can still connect your Xbox to other inputs in the reciever and get 5.1 from your games on Xbox.