Hi Tim,
This can be a very frustrating situation, and in the end you may not be able to do anything about it. You didn't mention what kind of radio you're using, however I'll assume it's something decent. Although the nearby powerlines may be the cause of your problems, there might be a few things you can do to rule out other possibilities too.
1. I'm assuming you can power your radio from batteries; do you get the noise when the unit is powered this way instead of being plugged in? Does your vehicle also get the same noise (both running and when engine is off)? Car radios also generally have better shielding so this test might be quite telling if the offending signal is coming in via the antenna or by another means on your other set.
2. This requires some work, but you can rule out something in your home by turning off the power at the mains. Keep in mind that you'll affect a bunch of systems in your home and that clocks etc. will need to be reset afterwards. Check your radio again with the power in your home off. Sometimes the culprit is right under your roof...
3. Take a drive around your neighborhood while listening to AM and see if the problem is widespread around your area or localized near your home; again the problem might be a bit more local than the power-lines.
4. Contact the stations directly and ask them if they have any reports of similar interference for your area.
If it looks like the problem is indeed widespread for your area (and out of your control) then you'll be limited in what you can do, however you may have some luck using an antenna with some directional properties to it such as a loop. This can be rotated to "null" out the offending noise in some cases; of course this will only be of use if the stations you want to listen to are located accordingly.
