Does anybody know what to do for federal return when it says "TOTALSTATE" on one of the State identifiers, when State abbr. is blank?

Yes, you need to report OR.

Totalstate means you have state tax and/or state withholding from more than one state.

Enter OR information as a different line on your W2:

1. Type w-2 in the Search box in the top right
2. Click on Jump to w-2
3. When you enter GA state details select Add another state and add information for OR. 

So, basically, I file - 

• Federal and give them info for Federal, GA, as well as OR.
• GA (resident) State
• OR (non-resident) State

Do I add the details from Copy B that has Totalstate or Copy 2 that has OR details?

If you lived all year in GA, you will file GA resident return and OR non-resident return.

Add OR details from copy 2 by adding another state line on your W-2. TurboTax will carry over the information to your state returns. 

When you get to the state returns, always prepare the non resident return first. 

How do I file a nonresident state return?

Oh! Any reason I should do that first? Just cause I haven't done it yet.

You state of residence might give you credit for taxes paid to another state.