I´ve met people in Laos and Cambodia, who have bought Minsks in Vietnam and ridden them out of the country. So maybe its possible (getting a foreign bike into Vietnam is a pain, very few have managed to do that). The Minsks are old Russian bikes, so will require quite a bit of maintenance. I would consider twice going on a long trip with one.
If you get out of Vietnam then Laos, Cambodia and Thailand are do-able, but after that you will find you wont get into Burma with the bike. China is possible from Laos, but will require much more than just going to the border and entering. The usual way is to freight the bike between Thailand or Malaysia and India or Nepal. Search this site, and you will find more information about those.
And if you are taking a foreign bike to India, Pakistan or Iran, you´ll need a carnet to be able to import it temporarily. And you´ll probably need to have your name in the bikes´ papers to cross any borders in SE Asia.