Another question I answered myself!
Since I bought a house, I get annoyed by the journal Current Quests added with it: http://elderscrolls.wikia.com/wiki/My_Imperial_City_House. I did a search for "oblivion console mark quest as completed" which I didn't find anything interesting. The closest I came to a solution was http://vgstrategies.about.com/od/pccheatso/a/OblivionQuestIDCompletion.htm but the 1st command "qst" gave me an error the command was not found then I tried "ShowQuestTargets" and it did display something in which the intelligible part was "Active quest: HouseImperialCity". I moved further on the about.com page to
but entering "SetStage HouseImperialCity 100" did nothing ; the quest was still in the journal active part, it wasn't in the completed part neither any furniture was added to the shack/house. I didn't want any furniture added, just the quest marked completed. So I did a search on the quest ID and didn't find anything of worth for me but then I quoted the name (https://duckduckgo.com/?q=oblivion+quest+%22HouseImperialCity%22) and I went to http://tes.ag.ru/oblivion/quests/houses.shtml ; I don't understand any Slavic language so I prepared myself to have it go through an online translator. I was happy to find out around the searched quest id some English:
So the problem was that I had to set the stage to the maximum of that actual quest, which was 30.