B737 suffered loss of air data computer system and associated indicators in IMC condition.

Narrative

During descent on the Delta Three RNAV Arrival in SLC; approaching FL190 with the Co-pilot flying; and in a VNAV path descent; both pilot flying displays showed 'IAS DISAGREE' amber alerts. The Co-pilot airspeed indicator had rolled back to 217 KTS while the Captain's airspeed indicator read 280 KTS. The autothrottles disconnected and the IAS/Mach display on the glare-shield indicated character A (under-speed). This was followed by the 'Altitude Disagree' amber alert display on both pilot flight displays. We then noted an 800-foot difference in altimeters. The true air temperature indication above the engine instruments was blank and replaced by horizontal dashes. 'A/T LIM' was indicated above the primary engine instruments. Looking on the overhead panel; the engines had reverted to 'ALTN' amber mode with the 'on' light extinguished. We were IMC with light to moderate turbulence with significant convective activity in the vicinity. I assumed control of the aircraft from the Co-pilot after we both confirmed that my instruments were reading correctly when compared to the standby instruments and crosschecked the angle of attack. I declared an emergency with SLC Center stating problems with airspeed and altimeter indications. I directed the Co-pilot to accomplish the appropriate abnormal checklists followed by the normal checklists. I briefed the flight attendants on the situation and to insure all passengers remained seated after landing. We were not able to recover the failed instruments but a normal approach and landing was made. We did not exceed any engine or airframe limitations. Appropriate aircraft logbook entries were made and the malfunction discussed with maintenance and oncoming co-pilot. Maintenance reported the failure of what appeared to be an air data inertial reference unit (ADIRU); and failure of an air data module (ADM).