An MD80 landed under emergency conditions when burning odors were detected on board.

Narrative

On departure; while climbing in icing conditions with engine and wing anti icing on; a burning plastic odor presented in the cockpit and cabin. We turned off galley power and cabin recirculation fan; but smell continued. Shortly after turning off engine and wing anti icing; the odor abated. We concluded that the cause was something to do with anti ice system. We called Dispatch to advise and requested a mechanic meet the flight. We returned galley power and recirculation fan to normal operation.On descent; prior to entering precipitation; Flight Attendants once again reported smelling the odor; and that was corroborated by First Officer. We took initial steps of donning O2 masks and establishing communication; turned off galley power; recirculation fan and high pressure bleed off on AC packs. we declared an emergency with ATC and requested priority for Runway 30. I communicated with the Flight Attendants to keep me advised of any changes in the cabin odor and that we were getting priority handling. I briefed them for a normal landing and no evacuation unless the situation deteriorated. Finally; I made a PA to the passengers to explain to not be alarmed if they see airport safety equipment around the aircraft after landing.The First Officer made a normal landing and we rolled out to end of runway where CFR looked us over and advised all was normal. We then taxied to the gate.