I was wondering what is the best possible connection i can make to connect the computers audio to my onkyo reciever.
The "best possible connection" is a digital one. That will allow you to use the DACs in your receiver that are almost certainly better than the DACs on your PC's soundcard, both from a spec and listening point of view. There are also cheap amps in the preamp section of the soundcard that will be bested by your receiver's. Finally, there is EMI and other noise in a PC that's just not good for an audio signal. I have to use my an analog out for my zone 2, and I get a slight hum from that signal. At the same time, and from the same sound card, I also use an optical digital output. That's silent, and decoded by my preamp for both stereo and Dolby Digital and DTS listening (5.1).
I have a 7.1 setup home theater setup in this room, and i was wondering what cables/ jacks i should use in order to get the maximum quality between the two.
It sounds like you want to use 7.1 in that room. If that's the case, your receiver is generally going to decode that, and I doubt you'll get the decoding from the sound card (the rear two channels of a 7.1 system are generally synthesized from the original 5.1, with some exceptions for DTS NEO:6, I think). Even if you do allow the sound card to decode, you'll have to run eight analog cables from your soundcard. You will have to rely on your sound card or your sound card's drivers/software to do the decoding, thereby losing the power of your receiver's processing capabilities.
A digital connection requires only one cable: either a TosLink optical cable or a coaxial cable (looks like a single RCA cable). You may need an adapter of some type or another, which will cost about $5 at RadioShack.
If you don't have digital out, I would recommend you find a digital sound card. Unless I had sought out and purchased a fancy-schmancy 7.1 sound card ($$$$, and it sounds like you haven't), I would not consider an analog connection from PC to receiver at all. You want a digital connection.