There was a while back an interesting piece in the paper about a theory that the electrical charge near high voltage power lines can exert an attraction for certain particles; breathing in the relatively higher concentration of those may be connected with these reported illnesses more than any purely electrical or magnetic effect, which, as several people have pointed out, should be more-or-less self-cancelling.
The particles mentioned were certain pollutants from hydrocarbon incomplete combustion but also certain naturally ocurring alpha emitters such as radon gas were measured in higher amounts near the lines.
There has been no proper collection and analysis of data yet to measure the exact particle levels in these "illness cluster" areas, actually in people's dwellings and offices, but it certainly sounds like an promising theory, so those investigations will be interesting to read about.
Myself I did not like to live too close to them beacuse of the noise when it was damp or wet weather, fizzling and buzzing, and because of the disagreeable ozone smell, which is also, it is said, very bad for lungs.
