Lamp buzzing when off, only on two specific sockets
If it's buzzing, it's not off.  

Often this is a dimmer that is not QUITE off. For instance dimmers often have free-motion inside the dimming range, then a stiff detent before bottoming out at hard "OFF". People often think the bottom of free-motion is off, and they never realize to push past the detent to actual "off".  It would be a lot weirder if you had a dimmer on a dimmer, and adding an LED/CFL to the mix gets weirder still. 

When you say "only does this on two sockets", that comes back to the theory that these are sockets which are switched from a light switch somewhere.  If it's not dimmed, and it shouldn't be, there could be trouble in that circuit.  

If a light switch works a receptacle, it can't be a dimmer unless it uses a weird receptacle keyed to only accept lamps. 

Does everything plugged into those sockets buzz?  Or only that one lamp? 

If a dimmer is not involved, then I'd say you have an electrical problem of some serious concern.   A lot of newer electrical work is done very cheaply, with the 60 cent builder grade receptacles instead of the $3.00 goodies, and with "back stab" connections instead of screw terminals or screw-and-clamp.  In that case, take apart the receptacle and change it to a quality receptacle with screw or clamp wiring.