How would the CASE statement look?  Would it be a case for each column, something like this?:

SELECT CASE WHEN pickup_address < dropoff_address THEN pickup_address ELSE dropoff_address END AS address1,
CASE WHEN pickup_address < dropoff_address THEN dropoff_address ELSE pickup_address END AS address2,
CASE WHEN pickup_city  < dropoff_city THEN pickup_city ELSE dropoff_city END as city1,
CASE WHEN pickup_city  < dropoff_city THEN dropoff_city ELSE pickup_city END as city2,
CASE WHEN pickup_Lat < dropoff_Lat THEN pickup_Lat ELSE dropoff_Lat END as Lat1, 
........
FROM YourTable