As you only need to worry about two dimensions (x and z) for character movement, some simple trig should solve your problem, use this overload of the function:
void FulcrumPhy::moveCharacterController ( int id, float X, float Y, float Z)
Use this next piece of code to get your X, Y and Z values and put them in a dispacement vector:
NxVec3 displacement(dbSin(dbObjectAngleY(id)) * speed, gravity, dbCos(dbObjectAngleY(id)) * speed);
If you get that working for forward movement you should just be able to add 90 to the object angle and your character will strafe.
EDIT: You could also just turn your character, move, and then turn it back, buts thats a bit of a hack