What is the actual product you have? I'm having a hard time finding a manual for what you listed as your purchase. There is a bunch of info on the DAV-DZ175, but not the HBD-DZ175 that you listed.
https://www.sony.com/electronics/support/res/manuals/4165/41654831M.pdf
It concerns me that you may have an all-in-one system without a powered sub and speakers which are not entirely compatible with most standard systems.
If this is the same thing...
https://www.ebay.com/p/Sony-Hbd-dz175-DVD-Home-Theater-System-Receiver-Main-Unit-7834/16018471824?iid=132862914648&chn=ps
Then your subwoofer is non-industry standard and it won't connect to any standard A/V receiver from any company because it is a non-powered sub.
Your other speakers would need the proprietary Sony ends cut off and then connected to the industry standard speaker outputs of a new standard A/V receiver.
The speakers are all 2 5/8" size rated at 3 ohms. Which is lower than most receivers typically driving, but shouldn't be an issue at lower volume.
You can see on the back of the receiver that you linked to that it recommends speakers between 6 and 16 ohms, so the 3 ohm speakers could present an issue.
It would be better to get something like this for a bit more money...
https://www.accessories4less.com/make-a-store/item/yamyht3920ubl/yamaha-yht-3920u-5.1-ch-home-theater-system/1.html
Replace the speakers and the subwoofer. You can't use the subwoofer cable if that was run in the wall because that is NOT industry standard, but you can put it near the receiver. The rest of the cables you can cut and splice in the new speakers just fine, though if you used the stock Sony cables they are undersized and are likely of improper gauge for the distance in use. But, that's what it is.