Little Bikes are Simple
No license is necessary for motorcycles under 50cc, or electric bikes (e.g. Australian Embassy). You may, however, struggle to find such a bike for rental; electric bikes might be possible to get hold of in the big cities, but you're not going to be going on a road trip on one.
The Law on Bigger Bikes
For bigger bikes, or cars, it's more complicated.
Vietnam is a signatory to The Vienna Convention On Road Traffic (1968). It is also a signatory to the 1949 Geneva Convention, but that doesn't seem to matter here (which is important later).
then according to this circular from the Vietnamese Ministry of Transport, you may use it from 1 October 2015. (The signed original is here, but it's harder to translate.)
Thanks to @nhahtdh, the translation of Section 11 says:
Article 11. Using the international driving permit from the countries participating in the Vienna Convention issued in Vietnam
- Holders of IDP issued by participating countries of Vienna Convention while operating a motor vehicle in Vietnamese territory must carry the IDP and national driving license in accordance to the classfication of vehicle under operation; must comply with the road traffic law of Vietnam.
- If the IDP is retained temporarily in violation of road traffic law of Vietnam, the retention period may not exceed the driver's permitted period of stay in Vietnam.
Why the Conflicting Advice?
Many countries are not signatories to the Vienna Convention - Australia, the US and Canada are notable examples, and this is presumably why their travel advice tells you that you need a local license. According to the circular, your license is not valid. Only licenses issued by participants in the Vienna Convention are valid, so yours are not.
European countries tend to be signatories, and this is why France and Germany for example will tell you that an IDP is accepted. The EU countries negotiated for this reform, and are happy with the situation.
Enforcement and Recognition
I can't comment as to whether this distinction between Vienna Convention countries and others is effectively enforced, or whether IDPs are accepted in practice by your average member of the traffic police. I would not want to be the first person to be pulled over by a cop in a rural area who hadn't seen this sort of thing before.
From a report on a local (closed, hence no link) Facebook group, even if you have a motorcycle license from your home country but no IDP, you may get pulled over, and your bike impounded. In this case, they even reportably refused a bribe. This is still rare, and the fines - perhaps around $150 - small by Western standards, but it does happen.
From personal experience, the traffic police in Hanoi are more active now than they were a few months ago. This is a good thing, but maybe not if you don't have a license.
Getting a Vietnamese License
It is possible to transfer an existing motorcycle license into a Vietnamese one (and similarly for cars). New Zealand has some detailed advice - it involves notarising your license, getting a bunch of passport photos, and waiting for a week or two. Going through an agent might be easiest - I had someone do most of the legwork for me, and all I had to do was show up to have my photo taken.
Alternatively, the test doesn't look too hard. The Theory Test may sometimes be available in English, although other sources say it isn't. If it's in Vietnamese, an agent is likely to be able to provide some tips...
In either case though, this isn't something you'll be doing on a short holiday here!