error: invalid input syntax for type integer: ""

ERROR: invalid input syntax for integer: ""

"" isn't a valid integer. PostgreSQL accepts unquoted blank fields as null by default in CSV, but "" would be like writing:

SELECT ''::integer;
and fail for the same reason.

If you want to deal with CSV that has things like quoted empty strings for null integers, you'll need to feed it to PostgreSQL via a pre-processor that can neaten it up a bit. PostgreSQL's CSV input doesn't understand all the weird and wonderful possible abuses of CSV.

Options include:

Loading it in a spreadsheet and exporting sane CSV;
Using the Python csv module, Perl Text::CSV, etc to pre-process it;
Using Perl/Python/whatever to load the CSV and insert it directly into the DB
Using an ETL tool like CloverETL, Talend Studio, or Pentaho Kettle