The Finnish pronunciation is [MEER-yah] with a rolled "r." For a spoken pronunciation by a native Finnish speaker: http://www.forvo.com/search/Mirja/ [noted -ed]
I guess I'm the only one with the name, Hahaha. Well me and my mom :) My Grandpa brought it to Nicaragua, after World War II. I never really liked it or disliked it. But it is unique. I get called Mia. :)