It's not an oscillation, it's just that if you land with alot of rudder and keep it in, the nose will dart off in the direction of the rudder pedal input if you put weight on the nosewheel suddenly.
I'm a relatively new Viking pilot (~75 hours) and I've only experienced the "oscillations" once.
All I did was pull back on the yoke to get the nosewheel off the pavement, straightened the nose with the rudder, then let the nose gently settle back down by itself, knowing that as the nosewheel tire began to grip, I would need to straighten out the rudder pedals.
This happens because the nosewheel steering is directly coupled to the rudder pedals, unlike other types that have springs/bungees that allow the nosewheel to caster a bit. Vikings aren't the only plane like this, Saratogas have the same issue, so I have been told.
All you do is to land nose-high (you know, like you're supposed to but few tricycle-gear pilots ever do) and keep the nose up with back-yoke until the plane slows to 40mph or so (without brakes), then ease forward on the yoke and be prepared to change your rudder pedal pressure as the weight transfers to the nosewheel.
A Viking is not a C-172, but, why would you want it to be?
I don't think I would ever land on a short (<2500 ft.) paved runway with a significant (>15 knot) crosswind without practicing on a longer runway first. It seems it will take a bunch of practice to quickly transition from rudder-steering to nosegear-steering and then get on the brakes without causing the nose to dart-off to one side.
YMMV
