There is something called AGC, Automatic Gain Control, that is in all radios, it turns down the gain for large signals.
If you were 1 meter from the antenna you would receive more RF power than would be safe. However, you need to recognize that power is transmitted in all directions of it is distributed around the antenna(s). Now if you were 100 meters from the antenna, the power level would be much smaller. In addition, most good FM receivers have an automatic gain control circuit to reduce the gain if the signal is too large. This is why the receiver is not overloaded.
You did not understand the basic FM radio circuit function. Antenna capture signal from space. The tuning circuit select the frequency to be passed. Signal goes into mixer stage to beat out an IF 10.7mc in FM. Finally reaches to the detector stage to chip out top and bottom parts carrier waveform to remove all the noise and take out the audio signal. Since RF signal has been passed so many process stages,overload never occur. Besides, it also has a AGC circuit to control the overall gain in those IF stages automatically to avoid distortion.
If you were one meter away from such a large transmitter, your radio probably would explode! Imagine (or try) what would happen if you put your radio inside your microwave oven, which puts out 'only' 1kW (or so), your radio will quickly blow up.
An fm radio transmits at 250kw the amplitude is constant . At any distance the inverse square law takes affect and the power of the radio wave is decreased. If i was standing one meter from the fm transmitter why doesnt my radio recieve the full 250kw of amplitude and explode into a thousand pieces. Is the signal attenuated first? If so how? circuit diagrams would be helpful, or links. Also if i recieved power could this be converted into a voltage and a current, as V * I = W or is it just voltage peak to peak ? Thanks