this motor is a whirlpool dishwasher # 3377333 forward reverse type on a kenmore 665.15973992 or the clone whirlpool 7du920pwk so

what resistance should be measured across the 4 terminals to each other and to chassis? Thank you in advance

It should be open to chassis, never any reading. You have common and the speed wires, so between the common and the speeds they will get progressively higher as you go from high speed to low.