I went onto my account on another PC to look at my 'Inventory'. What kind of struck me was Oblivion and Morrowind not listed plus Skyrim as some kind of offer on a trade market or something?

I contacted Steam support (yes, you need three accounts, one to play, one to buy stuff and one to get help) and now two days later:

Thank you... bla... please provide a screenshot...

Now lets see what the answer will be next week, to the screenshot I provided 30min later.

I feel like I'm missing something here. Are you asking for help, opinions?

I've had good experiences with Steam support. They should be able to help.

One question though, my games show up in my Library. Inventory is something different, I believe. There are trading cards in my inventory.

http://steamcommunity.com/tradingcards/faq/

https://steamcommunity.com/tradingcards

Not all games have cards. The only ones I have showing up are for Skyrim. Since I usually play offline, I don't get the cards normally which doesn't actually bother me.

Your Inventory is not your Game List (Library).

Thanks! No idea what playing cards are, but I am going to close the ticket then.

I only opened a Steam account for Skyrim and bought the Oblivion and Morrowind there out of convenience there (but found my original DVDs in the meantime).

I'm not exactly sure what you mean by that. The Support does indeed requires a separate account, but for playing and buying games on Steam, you use single, same account.