We ran into this issue with our system a few months back and worked with Dev at Synconics to get an app developed. They have released it, and newer versions, on the app store. It allows you to store, authorize, and validate credit cards from the backend on Sales Orders and Invoices. Also allows for refunds when needed. I highly recommend it: https://apps.odoo.com/apps/modules/10.0/authorize_net/

Details: On customer account, you link with Authorize.net and store a credit card (within Odoo backend screen). Can also store multiple cards per customer. On sales order, you can confirm with Authorize. You select the credit card on their account and if you want to just validate the card, or validate and capture payment immediately. If you do not capture payment, when the invoice is made, you then have an option to capture payment and get the money at that point. You do not have to leave the sales order or invoice screen to accomplish any of it. All of the data is store with Authorize.net and is just linked to your database for security.

So it sounds like I need to upgrade to version 12.  I am on 11CE. 

Do you think if I am using a gateway which can store a customers credit card, there would be a easy way to recall the stored credit card information via tolkens from the gateway to charge a repeat customer?

My customers like to email me order, so I create them in Odoo, and I need a easy to to bill their card.  I also need a secure way to store the card details. 

Which version you are using ? If you are using V12 then it is possible. V12 having functionality so you as a Sales Person/Manager go to portal view(with the use of Preview button on quotation), on behalf of customer you can pay the order using payment acquires.

And yes no need for website( customer stored card not accessible).