From a practical standpoint, (if you have to do this at all - say, if it's part of the funding requirements from the big-boss) I would agree retractable wheels - ideally with the "failsafe" position being retracted in case of power failure. This means that under most circumstances you stick with normal biped locomation - the wheels are for rapid transport on roads or pavements, when you don't have the time or room to call in a dedicated transport unit.
For stability, go with 3 wheels per foot - perhaps one behind the heel, and one either side of the toes? This also determines where the wheels retract to (2 at the top/front of the foot, one behind the heel/ankle). A triangle is the most "stable" shape, the larger the better. However, having all the "drive" at ground level will cause issues staying upright - ideally you add some sort of jetpack or maneuvering thrusters to the torso to reduce the resulting torque. (This may also allow for longer and/or higher jumps to avoid un-skateable obstacles)
For agility ("strafe/change direction without the wearer moving the feet") I would suggest some form of Omni Wheel or Mecanum wheel.
Making it work on the different terrains is hard - we can't even get full-sized cars or even dedicated offroad 4x4s to relaibly operate without under the wide variety of circumstances you suggest, at least not without either swapping the wheels/tires out or scaling them up to tanks or monster trucks. This is going to require fairly large wheels, and possibly some sort of retractable stud/spike system to adjust the grip and footage to suit the terrain.