Uploading null email address
A NULL value won't be a valid email address, so you'll struggle to get this into CiviCRM. This is intentional - why store an email that's not valid?

Remove address by contact edit

Correct procedure is to remove the address you want to get rid of. When editing a contact, you should be able to click on the email section, delete the text in the email field, and hit save.

Does that solve your problem? Your question doesn't indicate why you'd want to store a NULL instead of just deleting the relevant email entry.



Remove addresses by SQL

Since you say you have a bunch of "bad" addresses, you can remove them via SQL. Accessing the underlying data in CiviCRM may have risks (eg other data might be associated with an address you delete), so this should be done with caution. Here's the SQL command to delete emails none@none.com

DELETE FROM civicrm_email WHERE email='none@none.com';


(If anyone can suggest issues to this approach, please do so in comments?)

Remove addresses via API

You can also use the API - slightly more complex, but you're updating CiviCRM via its proper interfaces and it will be better able to handle the business logic around removing related data.

There's an API explorer in CiviCRM at civicrm/api/explorer, and using the tools there you can compose API commands to do what you want. Example code is given in the API explorer for javascript, PHP etc. For example, to find then remove addresses none@none.com using javascript (works from browser console if logged in with appropriate rights).

CRM.api3('Email', 'get', {
  "sequential": 1,
  "email": "none@none.com",
  "options": {"limit":0}
}).done(function(result) {
  result.values.forEach(function(email) {
    CRM.api3('Email', 'delete', { "id": email.id });
  });
});


You could use the sample PHP provided there instead, via a custom extension or module.