Whistling radiator

Whenever the heat comes on in my apartment a few of the radiators make a really high pitched loud whistling sound like a tea kettle whistle. The radiators are very old, classic silver ones. One radiator makes a constant sound and another makes an intermittent almost breathing whistling sound. The second one also has a small leak at the valve. Is there something I can do about this or should i call a plumber, and how do I know what the plumber needs to do so I don't get ripped off?

One radiator makes a constant sound and another makes an intermittent almost breathing whistling sound.

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Sounds like the air valve vents are shot. These are the small things that screw into the side of the radiator. Replace them with new ones. Keep the adjustment in the open position after installing. They will make some type of 'breathing' sound when the steam is coming into the radiator and the trapped air is being forced out but will stop when there is sufficient steam in the radiator and the heat activated diaphragm closes. When the radiator cools the diaphragm will open and as the steam condensates and goes back to the boiler air will rush back in.

The second one also has a small leak at the valve.

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You didn't say which part of the valve leaks. If it is where the valve meets the radiator try tightening the nut that couples the valve with the radiator. If it still leaks completely undo the nut from the threads and wrap teflon pipe tape around the threads and then tighten the nut.
If the leak is where the valve stem comes up through the packing nut try tighteneing the packing nut. This will make the valve harder to turn but should stop the leak. if it doesn't the packing is probably gone and you have to undo the packing nut completely and wrap packing thread around the stem where the nut tightens down. Or you can purchase complete new valve assemblies that screw onto the pipe that delivers the steam.
All of these steps are definitely do it yourselfable.