Can we use any of the Swedish 90°/45° Omni or Mecanum wheels in two wheeler configurations?
This started out as a comment but I ran out of space. Also, I am waiting for the question to be clarified, as morbo has requested of the OP.
Here is an example on YouTube, Lego Technic two-wheeled double track tank r/c omni-wheel, although I must say that the wheels do not look particularly omni to me:
Whilst this is not particular to Omni/Mecanum wheels, it is worth noting that a robot with a two wheeled differential drive can achieve stability if the center of mass is below the wheel axle or if there is a third point of contact striking the floor.
I suppose yes, one could. They are wheels after all.
This mostly depends on other things, such as your design and how you want to move (in actual omnidirection? keeping balancing will be difficult, but it is possible.) ...a wheel is a wheel, regardless of if it's an omnidirectional one or not.
An example of a spherical wheel being used in a two wheel system I've heard of is the omni directional motorcycle.