You can import orders as Cash On Delivery using the Transaction.gateway field.  EZ Importer doesn't support adding payments, so you won't be able to add payment details.

If you want to set the gateway as Cash On Delivery, you'll need to map the Transaction.amount field and the Transaction.gateway field like so:

Once you have the fields map, you'll want to set the transactions.gateway value in your file to cash_on_delivery.  Shopify is particular about your gateway values, so it must match exactly.

Cash On Delivery As A Default Value

If all the orders in your import are going to be Cash On Delivery, you can map the Transaction.amount field and set the Transaction.gateway as a Default Field instead of mapping it.  To set this up, ensure the Transaction.gateway field on the Transaction tab is not mapped (uncheck the checkbox to the left of the field name) and set the default field value to cash_on_delivery, as shown below.  The Transaction.amount should be mapped.

Once you have your configuration setup, you'll know if the order was correctly imported as cash_on_delivery by looking at your order's timeline.  

Financial Status

The financial_status and Transaction gateway are not tied, so you'll need to set this value if you want your order to be set to pending.  By default, Shopify sets the financial_status to paid.