B737-800
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Flight Crew Diverted; Flight Crew Landed As Precaution; Flight Crew Overcame Equipment Problem
Aircraft
Climbing through approximate FL250 in IMC and icing conditions; we got an IAS Disagree alert on the PFDs.  We noticed a difference between the Captain's and First Officer's airspeed indicators.  Shortly after; we got an ALT Disagree alert as well.  We realized the Captain's instruments and the STBY information were correct.  While we ran the Airspeed Unreliable checklist we coordinated with ATC for a block altitude of FL320-340 and a vector to the west to avoid the weather in the northeast.  At FL320 the Captain's and the STBY airspeed indicators were about 290 knots and the First Officer's was 150 knots; and the altimeters differed by about 800 feet.  We also had an ENG annunciation for the EECs in ALTN mode and completed that checklist as well.  We informed Dispatch and coordinated a divert to ZZZ1.  We [spoke] with ATC but required no further assistance.  We completed the Overweight Landing checklist--we would be landing just under 160;000 lbs.  Descending through about 16;000 feet on arrival the First Officer's instruments returned to normal.  We completed an uneventful approach and landing and taxied to the gate.
B737 Captain reported during climb to FL250 aircraft began to experience multiple Air Data Systems failures; compelling Flight Crew to divert to make a precautionary landing.