power cords with active shielding

Power cable hot and neutral conductors are carrying the same current in opposite directions being, in a sense, "balanced". Twisting them will make them exposed to external fields evenly causing cancellation. Same goes for radiated field from the cable. This works perfect as long as pitch of the twist is shorter than wavelength of the offending signal (4.9" for 2.4GHz). This makes practically no noise induction in ground wire. Twisting also increases capacitance (not important) and reduces inductance (important).

As for balanced circuitry - it does not reduce normal mode powerline harmonics the same way as balanced audio amplifier does not remove harmonics of the music - it only reduces harmonics produced by amplifier itself and only even harmonics (does nothing to odd harmonics). Balanced input supposed to reduce common mode noise. Power supply transformer does that already. Shield, in instrumentation/measurement amps cables, is usually driven with common mode input signal. This scheme eliminates capacitance between shield and signal wires for common mode noise reducing greatly capacitive pick-up. It works quite well, but I’m not sure if it makes any audible difference with power cables.

James1969, Yes, twisting signal wires will reduce it - if it is coming as common mode.  In the case of power cord your signal wires are hot and neutral (return).  Pitch of the twist should be many times smaller than wavelength (17" for 700MHz) Twisting them with 1" pitch should be fine but I would twist as tight as I can.  Noise might be getting in as common mode or normal mode.  Transformer should be good defense for common mode as well, but there is capacitive coupling between primary and secondary.  For that transformers have grounded shield (between windings).  You could also attempt to use common mode choke, winding power cable around toroidal ferrite core.  That would create inductance in series for the signals flowing in the same direction in both wires (common mode) but would be zero inductance (cancellation) for normal mode (signals flowing in opposite direction).  Unfortunately it is difficult to do (connectors, thickness of cable, etc.)  When noise already is or converts to normal mode you can't do much except for filtering.  Electrolytic caps inside present high impedance at these frequencies because of their high inductance.  Placing low inductance cap in parallel would help, but might create parallel resonant circuit with said inductance.  External filter should help but it might create big voltage drops since most of the gear takes power in short current spikes of very high amplitude.  That would appear as reduced dynamics of power amp.  I bought Furman Elite 20PFI conditioner that has power factor correction.  It supposed to present resistive load to the mains.  Other than very tight non-sacrifitial over/under voltage protection it has huge inductor and huge capacitor to deliver required current spikes to the load while presenting constant load to the mains.  With my amp (150W) it does not reduce dynamics. 

At 700MHz shield should be a good defense against noise, since anything induced would flow on the outside of the cable - shield, because of the skin effect.  The only problem might be shields inductance.  I suspect that better cables have better shielding in that respect.

James1969,  It is possible.  I had for few days CB like transmission loud voice coming thru pretty much everything at home - TV (turned off in stanby), speakerphone, radio.  I noticed every time the same unmarked car with many antennas passing by.  I suspect that his transmitter was out of whack.  FCC intervenes only when somebody complains.  Intensity of electromagnetic field drops in linear fashion with distance. When you are close it can be pretty strong.

Jim, speaker cables are antennas for the electrical noise since amplifier has low output impedance only for low frequency signals.  Induced noise enters amps input thru the feedback loop.  

As for the ferrite - on one hand you need highest permeability, but on the other high frequency response.  Self Resonant Frequency (SRF) specification might be useful since above this frequency impedance of the choke for common mode signals will drop like a rock.  Read this:
https://www.coilws.com/index.php?main_page=page&id=128

I've been once in the company that had so much of the noise pollution (multiple high frequency seem welders) that nothing worked - not even telephones.  Technicians there told me that common rules, like grounding shield on one end only don't even work. At the end they had to put every power cable in conduit.  We had to put our equipment, we sold them, in the metal NEMA box with metal mesh screen on the front door glass.

I did read everything but unfortunately cannot think of anything else, especially since Al and Ralph already commented.  It could be the power cable, speaker cables or both.  I listen to recorded noise and watched youtube video showing sound of different type of interference.  Judging by >1s gap between occurrences I would suspect that it might be intelligent power meter.  They repeat readings from each other for each household or apartment on "Mesh Network" at 900MHz few times a day.
Where is it located?  It could be also that it picks up all the sources - cell tower, trains, power meter etc.   What about getting metal conduit in Home Depot (it is cheap) and cut it to the size of power cable and speaker cables.  After running cables thru it ground them well.  Look for alternative grounds like faucet or radiator.  It is only to check what it is.  If noise goes away then we can start removing conduits one by one.  If it doesn't then either filtering from the Furman is too weak or amp itself is picking up noise and needs better grounding.  Most of shields are not perfect Faraday cage and have to be grounded in order to work.  For instance to make high frequency current flow on the outside because of skin effect (cable shield or metal box) it needs place to flow to - a ground.  Amplifier box should be grounded with separate wire directly to good ground.  I would experiment with different grounds.  If faucet pipes work, than running long ground wire is better than suffering from audible noise.  Perhaps speaker box also needs shielding? (Shadorne suggested it).  If it is difficult to do/check replace it with very small speaker (even plain individual) and shield it.