you need to use a CASE
:
LOAD DATA INFILE '/invoices/invoice1381301986.csv'
INTO TABLE invoice_table
FIELDS TERMINATED BY ','
ENCLOSED BY '"'
LINES TERMINATED BY '\n'
(`code`,@var1)
SET datefield= (
CASE
WHEN @var1 REGEXP '[0-9]{2}/[0-9]{2}/[0-9]{4}' THEN STR_TO_DATE(@var1,'%m/%d/%Y')
...
END
)