For UE nothing has changed, you'll get visa on arrival. But for Russian passports I think you need to apply for visa before. I'm not sure, so it's better to check. I googled two sources for you:
Russian consulate in Erbil: http://www.rusgencons-erbil.mid.ru/
KRG department of foreign affairs: http://dfr.krg.org/p/p.aspx?p=46&l=12&s=040100&r=370
Write to them and everything will be clear. Press is not a valid source in those cases.
But definitely if you want to go all the way to Jordan you need Iraqi visa, not only Kurdistan (everything to the south from Mosul/Kirkuk is not KRG anymore). South Iraq is still not a safe place to travel, so think twice before you go. Especially when there is also unstable situation in Syria.