Your airbox may be connected to the crankcase via the breather. If you are getting oil in the airbox, then it is most likely coming from the crankcase breather. This indicates some blowby. First, check to ensure you don't have too much oil in the bike. You can do this by placing the bike on centerstand and looking at the oil sight glass in the clutch cover. If the oil level seems normal, buy a compression tester. Warm up the engine and remove the spark plugs. Hold the throttle open and put the compression tester in each plug hole and kick the bike over several times to peak up the meter and record the reading. I am not sure what the service spec is for your bike but a Kawasaki Factory Service Manual or Clymers will tell. It should probably be around 150 psi. with no more than 10 ~ 15 PSI variance between cylinders or something like that. If it is less, then you have a ring problem. To verify, seal the rings temporarily by putting 1 tbsp of motor oil down each cylinder and checking compression in the same way, once again. ONLY DO ONE CYLINDER AT A TIME as oil will gush out and hit the ceiling on the cylinders not being checked. If compression jumps noticeably... say from 110 psi to 180 psi for this test, the problem is surely the rings. As an alternative, you can do a leak-down compression test but this requires a leak-down type tester and some expertise to pinpoint where air is leaking.
With the low miles, I would be surprised if you had a blowby problem but if the bike sat for a long period, moisture in the crankcase can get up into the cylinder bores and rust them making piston ring seal poor. You might try some Yamaha Ring Free or Seafoam in your oil to see if you can free the rings up to seal a bit better.
