B737-300 THOUGHT CLRED VIA LGA 7; WHITESTONE CLB. MUCH CONFUSION PRIOR TO DEP WITH DEICING AND WX. FO HAD COPIED CHANGE TO CONEY CLB; BUT IN THE DELAYS FAILED TO CHANGE THE FMC. CTLR CAUGHT THE ERROR AND VECTORED TO CORRECT RADIAL.

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AFTER TKOF FROM LGA RWY 13 USING THE LGA 7 WITH THE WHITESTONE CLB; WE WERE ASKED BY DEP CTL TO VERIFY OUR HEADING. WE REPLIED THAT WE WERE TURNING L TO 040 DEGS. THE CTLR SEEMED SURPRISED AND TOLD US TO CONTINUE TURN ALL THE WAY AROUND TO 230 DEGS. HE THEN STATED THAT HE HAD TRIED TO 'CATCH' US BUT WE WERE ALREADY IN THE TURN WHEN WE SWITCHED OVER FROM TWR. WHILE WE WERE CLBING OUT; THE FO REMARKED; 'I KNOW WE WERE ON THE RIGHT DEP; BECAUSE I WROTE IT DOWN.' HE THEN PROCEEDED TO SHOW ME THE SCRATCH PAD WHERE HE HAD WRITTEN DOWN OUR XPONDER CODE AND CONEY CLB. WE HAD RECEIVED OUR CLRNC VIA ACARS WITH THE WHITESTONE CLB AND A NOTATION TO VERIFY XPONDER AND CLB WITH CLRNC DELIVERY. THE WX IN THE PRECEDING 45- 55 MINS HAD BEEN CHANGING RAPIDLY; WITH; FREEZING RAIN; LIGHT ICE PELLETS; AND LIGHT FREEZING DRIZZLE. WE HAD BEEN DEICED TWICE; WITH 2 DIFFERENT TKOF HOLDOVER TIMES; AND HAD HAD TO CANCEL TAXI TWICE DUE TO BEING UNABLE TO LEGALLY TKOF. WE WERE TRYING TO TALK TO CLRNC DELIVERY WHILE MONITORING ATIS; COMPANY; DEICE; GND CTL; RAMP CTL AND OUR PUSHBACK INTERCOM; ALL AT THE SAME TIME. THE TKOF PROC HAD BEEN BRIEFED PRIOR TO OUR FIRST DEICE AND ALL THE APPROPRIATE HEADINGS AND ALTS HAD BEEN WRITTEN DOWN BY ME ON A SCRATCH PAD FOR REF TO AFTER TKOF. DUE TO OUR WORKLOAD I WAS MONITORING GND CTL WHEN THE FO GOT THE AMENDED CLB CLRNC AND IN THE RUSH TO GET AIRBORNE ONCE WE WERE LEGAL TO DO SO; WE BRIEFED THE ORIGINAL CLB (WHITESTONE) WHEN WE WERE #1 FOR TKOF. SUGGEST WHEN WORKLOADS GET THIS HVY; THAT ALL CLRNCS BE MONITORED BY BOTH PLTS AND THAT IF A DEP IS SUBJECT TO CHANGE; THAT IT BE GIVEN VERBALLY AND NOT PUT IN THE ACARS CLRNC AT ALL.