Train trip from Stockholm to Hamburg via Copenhagen next week (amid closures due to migrants/refugees)

For starters, I just had a look and found an SAS flight (ARN - TXL) using Kayak/Expedia for USD 118.29 - the second bag costs 45 Euros extra. Sounds like a fair price to me.

Then, your situation is a bit difficult as nobody knows if the border will be open on Tuesday or not. Hence, DB may not offer free-of-charge cancellation ahead of time. If you bought a DB saver fare, then you can always cancel it for a 17,50 Euro fee (before its first validity day), but your would also have to cancel the SJ trip seperately, which may also incur some fees. I am assuming that you did not buy a "regular price" ticket for the DB, which can be cancelled free of charge (before its first validity day), and you I also assume that you bought a non-transferable print-at-home ticket (which are much easier to cancel than transferable paper tickets).

Note that not all trains Denmark<->Germany seem to have stopped running! This thread at ice-treff.de (warning: in German) states that the Danish "IC3" trains are running between Flensburg and Denmark. There is also a Bus operated by DB that runs from Copenhagen to Berlin (link in German, link in English). You should be able to use your ticket on such an alternative route, but you may want to get a written confirmation in Copenhagen that your connection is not running in case you want to risk it and use your train tickets.