Err...
Right, so your speaker wires are acting as an antenna. Possibly the circuit to feed the 'phones is lower quality than that for the speakers, possibly the speakers have enough noise in them to drown the rogue signal.
What we need to do is cancel the lower power signal. Fortunately this can usually be done quite cheaply
First off; are the speaker wires long? (over a metre?) If not, think about whether there might be another longer wire running close to the speaker wires which is itself acting as the antenna and inducing the signal onto the speaker wires. (think ethernet cables, mains cables - including cables in the wall) If you think so, try moving the speaker wires away from the other cables, as this may reduce the problem to the point where you don't notice it.
If your speaker wires themselves are either all long, or one is long, try repositioning the speakers so that you don't need such long wires. You needn't replace the wires, but if you can try coiling the cables. Go for a coil in a flattish sausage shape, about 3 to 5 inches long, coiling as much into this lump as possible. Coiling like this can make the noise cancel itself if you're lucky, and also reduces the possibility of the cables acting as a good antenna. (longer cables make better antennas for radio frequency)
Last resort to fix the problem;
If you can find them, you used to be able to get little toroidal magnets for cancelling Citizen's Band transmissions (I'm speaking from the UK, but the concept is the same) Essentially you wrap the wires to the speakers around the magnet (making a transformer, basically), in a winding configuration. (its hard to explain this, face to face I'd draw a picture...)
If you do this on each of the wires (you could try one at a time, start with the longest wire), you might find that you can cancel the noise that way. Try this last as it costs money. You might be able to find the magnets at a decent hi-fi store, or somewhere like radio shck (in the UK i'd say Maplins, but I don't know if you have those where you are; basically the kind of place that sells electrical components for you to build your own stuff) If in doubt ask at the hi-fi store (they might even lend you some to try first) find out what the things are actually called then try to find a cheaper source.
Beyond that, your options are better headphones or better speakers. Obviously if you have a friend with other headphones or speakers its worth borrowing theirs to give it a go before spending cash.
Of course if you live close to the transmitter for this radio station you will have a lot more trouble. But on the other hand in that case it might be worth getting in touch and telling them that they're interfering with your electronics equipment - they may give you a hand sorting it out if you talk to them nicely (at the least they'll have access to radio engineers who might offer better advice)
Good luck!
(amazing what you pick up working as an EMC engineer...)
