You can't use IF like that. You can do what you want with AND and OR:
SELECT t.first_name,
t.last_name,
t.employid,
t.status
FROM employeetable t
WHERE ((status_flag = STATUS_ACTIVE AND t.status = 'A')
OR (status_flag = STATUS_INACTIVE AND t.status = 'T')
OR (source_flag = SOURCE_FUNCTION AND t.business_unit = 'production')
OR (source_flag = SOURCE_USER AND t.business_unit = 'users'))
AND t.first_name LIKE firstname
AND t.last_name LIKE lastname
AND t.employid LIKE employeeid;