Which cables interfere with each other most?

A bit like asking how long is a piece of string.. it will entirely depend on what is connected to the cables, how it is designed, and how the cable is constructed. The best thing would be to purchase a handheld EMF meter... they can be had for not much money and you can see which cable is radiating interference the most.

From your description genereally I would keep mains cables separate from Ethernet cables and both separate from parallel runs of speaker cables... I would keep the solar panel (presumably inverter) cables well away from everything by a good margin... as they will almost certainly be very noisy.. again your EMF meter will confirm.. but measure when the sun is shining.....

That would need a visual.

get your AV power cables on one block. Network power cables on another and the hifi on another.

you want to play just music ?  

You should be able to plug out everything that's not contributing. Can you do that ? Is that possible ?  If it is, then identify what your other ones are doing, and what importance they have.

Identify what cables are the most important, and make a measure to  separate them from those that are not so important.

Most cables these days are big on shielding and are supposedly dozey doozey amongst others so shouldn't be a real concern.

My system doesn't seem as complex as yours, but in eyeshot probably very similar. Looking at the back of a fairly basic set up a muggle would rightly be baffled.

I have found the power cables to be the most sensitive from interference. Both from orientation and from proximity to other power cables.

Which cables interfere with each other most?

I'm glad to read your title post reads "which cables interfere ...." as opposed to the all too often seen here "what cables interfere ..."  

If my response makes no sense then ask yourself "what" you are doing here, or "which" you are doing here. Simple semantics. We good tho.