I would avoid writing Script Destination, and use just Script Transform + Flat File Destination. This way, you concentrate on the logical output (strings of data), while allowing SSIS to do actual writing to the file (it might be a bit more efficient, plus you concentrate on your business, not on writing to files).
First, you'll need to get denormalized data. You can do joins and sorts in the DBMS, but if you don't want to put too much pressure on DBMS - just get sorted data out of it and merge it using two SSIS Merge Join transforms.
Then do the script: keep running values of current Customer and Invoice, output them when they change, output InvoiceRow on every input. Something like this:
if (this.CustomerID != InputBuffer.CustomerID) {
this.CustomerID = InputBuffer.CustomerID;
OutputBuffer.AddRow();
OutputBuffer.OutputColumn = "Customer: " + InputBuffer.CustomerID + " " + InputBuffer.CustomerName;
}
// repeat the same code for Invoice
OutputBuffer.AddRow();
OutputBuffer.OutputColumn = "InvoiceRow: " + InputBuffer.InvoiceRowPrice;
Finally, add a Flat File Destination with a single column (OutputColumn created by the script) to write this to the file.