Lag(?) issues

    case 2:
      pinMode(sensorPin, OUTPUT);
      digitalWrite(sensorPin, LOW);
      delayMicroseconds(2);
      digitalWrite(sensorPin, HIGH);
      delayMicroseconds(5);
      digitalWrite(sensorPin, LOW);
      pinMode(sensorPin, INPUT);
      sensorRead = pulseIn(sensorPin, HIGH);

This code belongs in a function.

Your robot will be flying blind while this code executes. A timeout on the pulseIn call would be a good thing.

We still have no idea what the servoCase, sensorCase, or steeringCase values are, so we have no way of knowing if they are correct/sensible. And, as PeterH points out, numbers don't convey a lot of information.

Your code has no comments. Not a one. That does not make for maintainable code.