How to copy a specific string from a column to another

Ah, interesting.  Yes, that does change things a bit.  I am going to assume you want the three values in three different columns: Expense Code, GL Code, Invoice Number.  
We add three calculated columns, each set up to look for a different string and pull back all the text after that string up to the next carrige return (UNICHAR(10)) like so:

Expense Code = 
VAR _Code = "Expense Code : "
VAR _CodeLen = LEN ( _Code )
VAR _CodeMissing = ISERROR ( FIND ( _Code, 'DataTable'[Column] ) )
VAR _CodePosition = IF ( _CodeMissing, BLANK (), FIND ( _Code, 'DataTable'[Column] ) + _CodeLen )
VAR _CodeEnd = IF ( _CodeMissing, BLANK (), FIND ( UNICHAR ( 10 ), 'DataTable'[Column], _CodePosition ) )
RETURN
    IF ( _CodeMissing, BLANK (), MID ( 'DataTable'[Column], _CodePosition, _CodeEnd - _CodePosition ) )

GL Code = 
VAR _Code = "GL Code : "
VAR _CodeLen = LEN ( _Code )
VAR _CodeMissing = ISERROR ( FIND ( _Code, 'DataTable'[Column] ) )
VAR _CodePosition = IF ( _CodeMissing, BLANK (), FIND ( _Code, 'DataTable'[Column] ) + _CodeLen )
VAR _CodeEnd = IF ( _CodeMissing, BLANK (), FIND ( UNICHAR ( 10 ), 'DataTable'[Column], _CodePosition ) )
RETURN
    IF ( _CodeMissing, BLANK (), MID ( 'DataTable'[Column], _CodePosition, _CodeEnd - _CodePosition ) )

Invoice Number = 
VAR _Code = "Invoice Number : "
VAR _CodeLen = LEN ( _Code )
VAR _CodeMissing = ISERROR ( FIND ( _Code, 'DataTable'[Column] ) )
VAR _CodePosition = IF ( _CodeMissing, BLANK (), FIND ( _Code, 'DataTable'[Column] ) + _CodeLen )
VAR _CodeEnd = IF ( _CodeMissing, BLANK (), FIND ( UNICHAR ( 10 ), 'DataTable'[Column], _CodePosition ) )
RETURN
    IF ( _CodeMissing, BLANK (), MID ( 'DataTable'[Column], _CodePosition, _CodeEnd - _CodePosition ) )

My sample data has 3 rows that look like this.  You can see that the first entry only had the Expense Code so that is the only one that comes back.

It looks like you need to adjust the _Code VAR to match your real data.

Expense Code = 
VAR _Code = "Expense Code : "

This first VAR is set to the string "Expense Code : ",  this is the string it is searching for in the data but in your data it looks like the string is "ExpenseCode: " so you would have to change the measure to match.

Expense Code = 
VAR _Code = "ExpenseCode: "
VAR _CodeLen = LEN ( _Code )
VAR _CodeMissing = ISERROR ( FIND ( _Code, 'DataTable'[Column] ) )
VAR _CodePosition = IF ( _CodeMissing, BLANK (), FIND ( _Code, 'DataTable'[Column] ) + _CodeLen )
VAR _CodeEnd = IF ( _CodeMissing, BLANK (), FIND ( UNICHAR ( 10 ), 'DataTable'[Column], _CodePosition ) )
RETURN
    IF ( _CodeMissing, BLANK (), MID ( 'DataTable'[Column], _CodePosition, _CodeEnd - _CodePosition ) )