Just for me to understand. You have 4 Interrailpasses?
Then is no need to book the “Private Couchette Liegewagen” offer as this is a own special offer of Nightjet which includes ticket + reservation from 199€ :)

Usually if a group of 4 person book 4 couchette they will be next to each other by the system If you really wanna be sure it´s easier to call a booking office (for example of Austrian Rail) just say you want 4 Interrail Couchette reservations, train, route, date and ask if you could placed together. For the booking via phone you need a debit card :) 

ÖBB will book you in the same compartment and if that is not possible, then you'll see a warning before you pay, I noticed recently. But you'll have to use the ÖBB website to see that warning (using these steps). In addition, you don't pay Interrail's booking fees (2€ per person and train).

Thank you @seewulf and @rvdborgt for your reply. I finally got my reservation done now. Eventually the best way for me is to make the booking via phone. Let me share my experiences. :)

I tried to book via the ÖBB website and in the end there was a warning asking to accept that there are several compartments booking involved. So that's why I was afraid to continue.  Decided to call. When I called ÖBB the first time, the first ÖBB customer service said she cannot look up for me whether we can stay in the same compartment or not when I make a booking with Interrail pass. Strange for me. But she cannot help me with the same compartment booking. I almost gave up my plan.

So another day I called ÖBB the second time, now the second ÖBB customer service said the ÖBB website should book 4 of us in the same compartment and the warning I saw is general. I asked him to help me make a reservation anyway. Unfortunately he also struggled to make the reservation for me, because there was an error in their system. System just cannot book the same compartment automatically. He said it is their system error when booking for 2 adults and 2 kids. So he made a workaround to make the reservation for 4 adults instead of 2 adults and 2 kids. With 4 adults booking he managed to get the same compartment booking done. He also managed to get us the same price as 2 adults and 2 kids with a workaround voucher. So the same price as it should be. Good that I called :)  

Almost one hour for the whole call including waiting time before picking up and waiting for him to fix the system error. But it is worth it. Thanks to him, I can make the reservation right!  Hopefully this bug/error is fixed by ÖBB asap. ÖBB website booking should be more user friendly and intuitive in my humble opinion.