I'll be traveling to SE Asia, and want one phone service. If I buy a SIM card with Viettel in Vietnam, will it function in Thailand and in Laos and in Cambodia?
If it does, will I be charged roaming?
Yes and yes. There are no universal SIM cards in SE Asia, they all charge roaming fees, which can be quite expensive. It is much easier and more economical to get a pre-paid SIM card in each country as you travel. Or use voip services through your hotel's wifi each night.
As of 2017-01-11 Yes and partial yes.
There are no universal SIM cards in SE Asia.
However, from 2017-01-01, Viettel
removed reduced roaming charge in Vietnam, Laos, Cambodia.
The new fee can be found here (unfortunately it's in Vietnamese) in tab "Cước Roaming Đông Dương".
The new fee is: