Part of your question is relatively straightforward. Obviously DSP refers to the MCACC room/speaker calibration the Pioneer AV receiver uses.
To turn these effects off, select "Pure Direct" for your listening mode.
From the iControlAV5 iphone/ipad app, select Control > Listening Mode > Pure Direct. Or from the remote control, select "Receiver" then keep pressing the button marked "HDD" (it has "Auto/ALC/Direct" marked above this button) until the display reads "Pure Direct".
However, and this is quite a large "HOWEVER"; all this will do is turn off the MCACC room/speaker calibration.
As to whether you're listening to the Oppo's DAC or the Pioneer's DAC will depend on how you've got them connected and how you've set up each component within the menus.
Generally speaking, to hear the Oppo's DAC, you will need to use the Oppo's preamp and use the 7.1 analogue out interconnects to the Pioneer's analogue inputs. This way, the signal leaving the Oppo is analogue and the Oppo did the DA conversion.
However, if you simply have the Oppo connected using HDMI, then the Oppo simply forwards the digital signal to the Pioneer and the Pioneer will do the DA conversion. You'll also need to make the right choices within your Oppo's menu.
Obviously the simplest and box-free way would be to use your Oppo's preamp and connect it directly to your power amp and leave out the Pioneer altogether. Although I personally find the different Listening Modes really useful, swapping in between Pure Direct, Direct, Extended Stereo and Optimum depending on the source and type of music/movie I'm listening to and the time of day. As much as I like the idea of an Oppo to power amp set-up, in practice, in my room, I think the AV receiver does a really useful job and is highly tweakable.
I am a tad envious of your Oppo though, particularly as it has (or is about to have) Tidal streaming included. I also understand the headphone out is pretty decent, and I quite fancy using the stereo analogue outs (which I understand are excellent) into a Musical Fidelity M1HPAP for twin high quality headphone listening for all my music and video sources (by plugging my Roku's HDMI into the Oppo).
The Oppo's certainly the Swiss Army knife of the AV world.