How long would it take to travel from Saarbrücken to Stockholm using the train?
I'm able to make 1 stop if necessary.
And what route do I need to travel?
Apart from the regular travel search, DB also features a Sparpreisfinder (rough translation: cheap price finder). You will need to use the out-of-country one that I linked (hopefully the link doesn’t die), select Sweden as the country and Stockholm as the station. It features four options from Saarbrücken to Stockholm ranging from €139 to €169 if you don’t have a BahnCard (and are 31; I randomly put in an age because it asks you to and I didn’t want to risk youth prices).
If you can, you really should book a single through ticket. If you do, then it’s not your fault if you miss any train due to delays.
No matter how you do it, there is going to be a night connection somewhere. Since German railways do not see themselves as competent enough to offer night trains with sleeper cars, you are either restricted to a night in a sitting train or one at a station (one connection I can see has you wait 3:50 h in Neumünster — not exactly my definition of a successful night ;)). Of course, you can always break your journey into two, but you can’t book that via the Sparpreisfinder directly. However, if you set your eyes on a specific part in Denmark/Sweden, you can go back to the usual journey planner and select a stay of however long at a German station of your desire. You will still be able to book a through ticket.
The connections I got:
All this was plugging a random day.
You see that you get two general routes: Northwards to Hamburg and then either across the Danish mainland to Copenhagen or across the Fehmarn belt. The last leg is identical.