Right now, I think there is not a way to do it within Unity. This is what I have found so far (please, correct me if I'm wrong):
The most popular VR plugins compatible with Unity for both Android and iPhone are Durovis Dive SDK and Google Cardboard SDK.
I have read that most Android phones are compatible with those VR plugins. My experience is that just a few are compatible. Durovis Dive SDK seems to be the most compatible one nowadays. If the Android phone has not gyroscope and the game has the Google Cardboard SDK plugin, the game won't load or crash. If the Android phone has not gyroscope, the game will load but the image will be still when we move the phone.
Unity 5.3 has been just released. It includes WebGL support. It includes VR support. Samsung Gear and Occulus are supported. However, I have not found out anything about the compatibility with others Android or iPhone devices. Maybe it works (I have not test it. I have not found somebody who has test it yet).
We can find stuff to Export an Unity scene to Three.js. Scripts and animations don't seem to work though.