To assist our replies what dates are you looking at and on which site are you trying to make the reservation?

The date of the ride is the 17th of October, from Stockholm central to Oslo S, the train on my pass is in 7:36 in the morning and is a direct train. I tried making a reservation via the eurail website and also the SJ website, on both of them that train didn't show up at all.

Have you updated the app to the latest version? You should always trust the timetable of the national railways and not the app if there are differences. 

Just to be clear, it is the eurail app that is incorrect, it is always the eurail app that is incorrect. It is not a reliable source of accurate schedules and you should always use the websites of the local operator or the planners of operators such as bahn.com  that provide accurate schedules for much of Europe.

There is ongoing track work on the line east of Oslo and it seems they are relying on connections in Karlstad using commercial bus operators for the Oslo - Karlstad section. Your pass is not valid on these, although the price SJ quote for a passholder reservation is very high so it may include travel on the bus portion.

If you want to do the journey entirely by rail you will need to go via Gothenburg, the 06.24 departure being the only morning connection.

The 7.36 direct train is cancelled during some days including the 17th of October. 

Thank you so much to all of you, helped me a lot, I really appreciate it, and will not trust the schedule in the app no more!

If SJ cancelled the train, then I'd ask them what they propose as a replacement on your travel day, to use with a pass.