This gives me the forward vector of a Object3d
var forward = new THREE.Vector3();
object.getWorldDirection(forward);
How do I get the right-hand side vector of the object (using Three.JS)?
My best advice is to NOT include 'three.js' in your Google search when looking help regarding three.js.
I excluded 'three.js' from my searches and found similar questions by people in a Unity community...
Knowing this I found a very simple (admittedly very hacky) solution which works in three.js.
Take a plain-old right-hand vector
var right = new THREE.Vector3( 1, 0, 0 );
And just "turn it" by the object's .quaternion value...
right.applyQuaternion( object.quaternion );
Any (normalized) direction relative to the object's rotation can be gleamed in this fashion
Example: http://jsfiddle.net/9Lzx683v/