The very first thing to do is to try another power outlet box in the house -- one which is connected to a different phase of the power coming from the power company. Most homes have two feeds, each on a different phase. Also, make sure all of the fences are on one phase, while audio/video equipment is on the other phase. (A farm might have more feeds.)
The second thing to do is to install power line filters. Some industrial power strips which have surge protection also include high frequency filters. Tripp Lite Premium Isobars are one example. See http://www.tripplite.com/en/products/model.cfm?txtSeriesID=825&txtModelID=99
After you've eliminated noise coming in over the power lines, you have to eliminate the noise being picked up in the form of radio waves. Every wire in the electronics acts as an antenna. They all have to have filters added to them. The wires driving high-impedance loads are more sensitive to radiated noise than those driving low-impedance loads. Unless they're particularly long, the wires connected to the speakers themselves are the least likely to pickup the noise because speakers have relatively low impedance, Changing their size (gauge) won't make any difference at all. You have to eliminate the noise before it gets into the HTIB's amplifiers.
Unfortunately, blocking radio-frequency interference (like that generated by the fence power) is a big deal and has to be done by an electronics shop. It includes making the box(es) into Faraday cages.
1. adding copper mesh over all air-flow convection openings in the electronics boxes
2. making sure all seams are tight and making electrically conductive contact with one another
3. adding filters (ferrite beads) in the internal power supply leads
4. distributing additional filter capacitors in all of the equipments' DC power lines
Hopefully the first two suggestions (separate power line, filter noise in power lines) will reduce the noise adequately, though.