Using PIVOT to convert multiple rows and columns
Well, this solution is not particularly sophisticated (it doesn't use PIVOT), but it would solve your problem.  There are probably smarter ways to address the problem, but here is one method.

The solution selects from a derived unpivoted table (note comment about unpivot original data).  It groups by MyId and customer and uses CASE expressions to derive the individual column names and values.  My example only show two of the servicetype columns broken out into separate columns, but hopefully you'll see the pattern.  (I'm not sure how you handle the rows with blank servicetype).

--demo setup
DROP TABLE IF EXISTS supercharge
GO
CREATE TABLE supercharge (
MyID int
 , customer int 
 , Servicetype varchar(10)
 , servicerate varchar(10)
 , serviceNumber int
 , consumption int
 , daysofservice int
 , unitofmeasure varchar(10)
 , chargeAmount decimal(11,2)
 , chargeDate datetime  
)

INSERT INTO supercharge (MyID, customer, Servicetype, servicerate, serviceNumber,consumption,daysofservice,unitofmeasure,chargeAmount, chargeDate) 

VALUES 
(10016, 112992, 'RELC', '110W', 100, 753, 31, 'KWH',99.92, '2019-05-08'), 
(10016, 112992, 'RGAS', '120', 200, 0, 31, 'CCF',5.31, '2019-05-08'), 
(10016, 112992, 'RWTR', '130', 300, 3, 31, 'TGAL',11.85, '2019-05-08'), 
(10016, 112992, 'RSWR', '388', 400, 3, 31, 'NONE',10.12, '2019-05-08'), 
(10016, 112992, 'RGAR', '', 500, null, null, '',32.12, '2019-05-08'), 
(10016, 112992, 'STRM', '', 700, null, null, '',2.38, '2019-05-08'), 
(10016, 112992, '', 'LATE', null, null, null, '',15, '2019-05-13'), 
(10016, 112992, '', 'CUTO', null, null, null, '',30, '2019-05-08');

--solution
SELECT MyID
    ,customer
--RELC columns
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'rate'
                THEN value
            END) AS Relc_Rate
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'consumption'
                THEN value
            END) AS Relc_Consumption
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'daysofservice'
                THEN value
            END) AS Relc_DaysOfService
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'unitofmeasure'
                THEN value
            END) AS Relc_UnitOfMeasure
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'chargeamount'
                THEN value
            END) AS Relc_Charge
    ,max(CASE 
            WHEN Servicetype = 'RELC'
                AND col = 'chargedate'
                THEN value
            END) AS Relc_ChargeDate
--RGAS columns
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'rate'
                THEN value
            END) AS Rgas_Rate
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'consumption'
                THEN value
            END) AS Rgas_Consumption
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'daysofservice'
                THEN value
            END) AS Rgas_DaysOfService
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'unitofmeasure'
                THEN value
            END) AS Rgas_UnitOfMeasure
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'chargeamount'
                THEN value
            END) AS Rgas_Charge
    ,max(CASE 
            WHEN Servicetype = 'RGAS'
                AND col = 'chargedate'
                THEN value
            END) AS Rgas_ChargeDate

FROM
--unpivot original data
(
select MyID,customer,Servicetype, col, value
from supercharge
cross apply
(
  select 'rate', cast(servicerate as varchar(10)) union all
  select 'consumption', cast(consumption as varchar(10)) union all
  select 'daysofservice', cast(daysofservice as varchar(10)) union all
  select 'unitofmeasure', cast(unitofmeasure as varchar(10)) union all
  select 'chargeamount', cast(chargeAmount as varchar(10)) union all
  select 'chargeDate', convert(varchar(10), chargeDate,121)
) c(col, value) 
) d
GROUP BY MyID
    ,customer;




| MyID  | customer | Relc_Rate | Relc_Consumption | Relc_DaysOfService | Relc_UnitOfMeasure | Relc_Charge | Relc_ChargeDate | Rgas_Rate | Rgas_Consumption | Rgas_DaysOfService | Rgas_UnitOfMeasure | Rgas_Charge | Rgas_ChargeDate |
|-------|----------|-----------|------------------|--------------------|--------------------|-------------|-----------------|-----------|------------------|--------------------|--------------------|-------------|-----------------|
| 10016 | 112992   | 110W      | 753              | 31                 | KWH                | 99.92       | 2019-05-08      | 120       | 0                | 31                 | CCF                | 5.31        | 2019-05-08      |