Viking River's dress code is "elegant casual"--thus, no glitz, even for special events like the Captain's Dinner. The truth to tell, some women do dress up more than others...I even spotted a few sequins and crystals on our recent Eastern European Odyssey. However, sun dresses, pants suits, capris or slacks or long skirts and coordinating tops are the more usual choices. Men usually wear slacks and golf shirts, although an occasional jacket and tie are spotted.
As far as off-ship dinners and events, you'd have to take along appropriate clothing. if you were to plan to have dinner or tea at one of the fancier hotels in Hong Kong or Singapore or to attend an opera or go to the theater in any of the ports you will visit.
I kept a journal of one of our Viking river cruises, and it gives a fairly good picture of the ambiance, dress code, quality of food, and type of tours you can expect on a Viking sailing. Drop me a line if you'd like a copy.