Unfortunately it's not that easy to understand what you are exactly trying to book. Sleeper? Couchette? 

E.g. for the Hamburg to Stockholm SJ EN train: You can't book a private couchette compartment with a railpass. So the price shown for this is the normal price. That's why it is 4 times the price. For single beds in a couchette you do get a cheap price for passholder.

It's different if you did look for sleeper compartments. 

Snälltåget has just couchettes. It's possible to book a private compartment with them if you are holding a railpass (1.999 SEK).

Thanks for your answer. Yes I look for sleeper compartments... So better to take the snalltaget ?

As written before: Snälltåget has just couchette carriages. If you do like a real sleeper, then the SJ EN is your only option.

But then you shouldn't get such a price difference. But it may differ by booking date and options left. For concrete recommendations you should tell age and gender of your travel group and concrete dates.

In fact I would like to privatize a 6 berth cabin for the 4 of us. I read that we could take 2 extra children's tickets to do this. Do you think this is possible? We are 2 adults and 2 teenagers aged 14 and 17.

Thanks for your help

Not with SJ as you need a valid Interrail/Eurail pass for every traveller. With Snälltåget you can book a private couchette for the 4 of you.

SJ Euronight has 2 beds in the sleeper compartment so the 4 of you can book 2 compartment. The price with Interrail/Eurail is 830 SEK per person. Reservations have to be made at sj.se.

The domestic night train to Narvik has 3 beds in the sleeper compartments.