Wow! Don't do that.
I'd consider using twisted pair cables for all interconnects and even the speaker cables. I'd also wrap a copper braid shield around the bundle of audio cables, and ground it to a power strip at one end. I'd also make sure the strip filters out high frequency line noise.
The major threat is picking up the ac power (hum) through magnetic transference. The secondary threat is capacitive and other coupling by having the cables so close to each other, including two interconnects and/or speaker cables. The normal threat is picking up radio transmission.
Thin shielding is effective against radio transmission, but not magnetic fields. To stop a magnetic field, a shield needs to be more than an inch thick of iron alloy. The magnetic effect falls off quickly with distance, and is the main problem with putting wires close to the power line.
To inhibit magnetic interference from the power cables, consider using twisted pair wiring. It suppresses magnetic interference mostly by eliminating the distance between the two cables that make the circuit. (Beware a lot of misinformation on the internet that confuses general noise suppression of twisted cables in balanced lines. You only get magnetic suppression with unbalanced lines.) Interconnects shouldn't be too hard to find in any price range, or you can DIY. You can also find speaker cables made of bundles of twisted pair. There are a few expensive ones on the market, but you can DIY them much cheaper.
Since shielding is effective against radio noise, you can get the shielding effect by using a single shield around all of the audio conductors. Just ground the shield braid to the ground of the power line just after the filter. That one end should suffice. I'd probably use copper braid, but maybe it doesn't matter: I'd look into this. Any audio-specific power strip or box will have the filters and a grounding point, so it might be a good investment.
Unfortunately, there's also the issue of having all the audio cables next to each other, as well as the power lines carrying higher frequency noise--the house wiring acts like an antenna. Probably a filter on the power cables would help reduce that. There's also the braided shield between the power lines and audio cable to help reduce this.
I'm not sure how to stop all the interconnects and speaker cables from interfering with each other. Perhaps shielded twisted pair. If each pair were inside a shield, you could connect all the shields to ground at the same place where the other braid is connected. Be careful not to use normal shielded twisted pair interconnects--those have the shield connected to the signal return, which you don't want here. I'm suggesting a shield that's not electrically connected to any of the audio devices. Only to ground at one end. I'm not sure how much this helps. Perhaps you only need it for the speaker cables. It may be that you won't need it at all.
Heck, you might not need any of this. It's late, and I might have fallen off the deep end at some point while writing this, but I'm tired, so I quit.
