It is never a good idea to connect two sources to the same target (.i.e amp). The voltage from one source will feed back into the second source and cause damage to the circuits.
Few things you can try:
1. Connect a COAX digital cable from Oppo to Denon receiver. This is always much better than using HDMI if you are playing back 2-channel music. You will be using the DAC in Denon receiver.
2. Connect analog output from the Oppo to a source input on the Denon (like the CD left/right inputs). When playing music here, make sure to enable "Pure Direct" mode, so that the audio does not go through room correction. Any sort of room correction will require the Denon to convert analog-to-digital to process EQ and room correction, and then convert back from digital-to-analog.
3. Remove the Denon from the mix completely and connect the RCA outputs of the Oppo directly to the Sunfire amp. Then use digital volume control on the Oppo to control the volume. The Oppo has toslink, COAX digital inputs for audio as well as one HDMI input for another video source. The Oppo 105 is almost a HT processor in it's own right. You'll be able to use the DAC board in the Oppo, but you will not get any room correction.