How do I turn off this two-pipe steam radiator?
The item on the left is the steam trap and can not be regulated or shut off. stay away from this item. The shut-off valve is the item with the screw on the top. Turn the nut ccw (counter clockwise), just slightly about a 1/4 turn, then put a wrench on the stem above the nut, I would use a 6" or 8" pipe wrench or vise grips, and try to turn cw (clockwise) until it stops. This be the closed position. Do not put too much torque on this  stem. If you can't turn it, have someone that works on steam valves turn it. You do not want to break it or twist it off. After shutting the valve "off" turn the nut cw to tighten, not too tight.  You could also turn it part way to control the heat output if needed. If you still can not get this valve to close and want to control the heat output try covering the top with a board, cardboard, or wrap part or all of it with aluminum cooking foil. This is a steam system and the noise could be coming from above or beneath your apartment. Noise will travel in the pipes.   HOPE THIS HELPS