From BabylonJS version 2.5 Euler angles for use in mesh.rotation can always be found from a built in method. For some conventions of using Euler angles a quaternion can be found from those angles. Once found the quaternions can be used to rotate a mesh.
var yprQuaternion = BABYLON.Quaternion.RotationYawPitchRoll(yaw, pitch, roll);
Rotations alpha about Z, beta about X, gamma about Z around the world axes
var abcQuaternion = BABYLON.Quaternion.RotationAlphaBetaGamma(alpha, beta, gamma);
The Euler angles that can be used in mesh.rotation can be found from any quaternion the following method
var euler = quaternion.toEulerAngles();
To illustrate this the following playground generates three random angles, puts the axes XYZ into a random order and selects at random either to use world or local for all axes. This data is then used to randomise the orientation of a box. The rotationQuaternion for this box is used to generate Euler angles to rotate another box, box1, using box1.rotation to obtain the same orientation as the first box.