EC1198: reservations are only required across the German-Danish border. However these trains are always packed so you'll likely stand without one.

Copenhagen-Gothenburg doesn't have required reservations.

Gothenburg-Örebro has carriages with reservations and carriages without. @AnnaB will confirm. :)

Copenhagen-Göteborg, no reservations with Öresundståg, reservations mandatory with SJ high speed trains. 

Göteborg-Örebro, optional reservations with SJ regional trains. Seat 1-40 in carriage 2 are always unreserveable. Sometimes the whole carriage 2 is unreservable.

Thanks for these valuable inputs. Regarding trains in Sweden this does match with what I have read elsewhere: ‘in SJ-trains in Sweden, only intercity and high-speed trains have compulsory reservations’.

But it does leave me puzzled why authoritive sources like bahn.de and the interrail planner say different things. Giving wrong (and therefore contradicting) information does not help making railways the preferred alternative for everyone. One needs a train-insider for what should be a simple thing like planning a journey from Odense to Orebro.

It’s because there is no single authority. Each country and operator does their own thing and their priorities often do not include playing nice with their neighbours or making things easy for foreigners.

They run different reservation systems and send different amounts and types of data to the timetable database, some even provide false data on purpose.

I had the same question and asked SJ customer service by email. The first answer I got was:

“If it´s a train that you don´t need a seatreservation you can go with that train also. But you need to show the train attendants your Interail ticket.” Followed by a list of connections where seat reservation is not possible, As this was not the answer to my question I asked them again and got finally the reply:

“You can travel with  your interrail pass on Sj Regional without seat reservation as long as you travel in the correct carriage and not first class” which in the meantime was also given here.

I think bahn.de and oebb.at say for these trains are reservations compulsory, as regular tickets sold for such trains are usually integrated reservatiob tickets. I.e. you cannot buy a travel ticket without a seat reservation. The ticket is only valid on the booked train, like an airline ticket on the booked flight. Depending on the chosen fare it can rebooked to a different train or not. For travellers with single journey tickets this is more or less the same that “compulsory reservations”, for rail pass users not.

Meanwhile my journey from Netherlands to Sweden, through Germany and Denmark, has come to an end and just for the sake of any future travellers searching this community for tips and tricks, here we go:

• In Denmark and Sweden, seats can be reserved on many non-intercity trains but it is not obligatory. For the convenience of people travelling without reservation, the displays on the platform say where the *non* reserved seats are. Sometimes there are displays on the seats, but not always.
• As Denmark is the corridor to Scandinavia, consider making reservations for Hamburg-Copenhagen-Goteborg. However, if you have time, any train doing a part of this trajectory and that does not connect to a long-distance train before it, is likely to be less crowded (even half-empty). 
• For Sweden, get the SJ-app but while their live train info ('tracking') is great, the SJ train planner and reservation-tool are confusing as it will show you a cost of 35 SEK, while in fact this is the cost of an optional reservation. 

Unfortunately, the only ultimate answer is from the guards on your train. 

Seat61 has a very good summary https://www.seat61.com/interrail-and-eurail-reservations.htm

and the although it’s not great for itinerary planning or up to date info, the Rail Planner is good. But neither are infallible. 

Check with both, and here. If all are in agreement, you’re probably ok!