i have lived in myanmar for 5 years and can tell you that it is definitely IMPOSSIBLE to take a rented bike into myanmar, never mind where you would try to enter. the only ever way that bikers have made it into myanmar was with their own motorcycles and by special permit obtained from the government in yangon / rangoon. to obtain such a permit, you need to first appoint a tour operator (or similar) in yangon who will assume all responsibility during your trip in myanmar. this is obviously all very costly too.
as for laos, check out this website - it is full of information on how to get your bike in / out of laos.
As of Jan. 30, 2007 the Ministry of Tourism issued a new rule that said no foreigners were to be allowed to drive a motorcycle in Myanmar. See the exact quote of the other Myanmar thread. Having ridden there myself, I'd have to say there really wasn't that much worth going throuhg all the effort.. stick to Thailand, or Laos.