I also have oil back by the air filter box it drips down on the exhaust causing a little smoke cannot see where the oil might be coming from

 

Spitting,sputtering can be carb related or even cam related since the 98 falls with in the year models that were affected.Even a reverse limiter located below the terminal board can be faulting causing the hesitation. Simple to pull the black wire from it to see if it helps. Oil dripping on exhaust could be from the valve cover that you need to pull anyway to check the exhaust cam lobe and valve clearance. The oil tank has a vent line leading to the air box also. The air box has a foam piece that's supposed to soak up oil mist from the tank vent but check it out.This old style box had a habit of breaking off lid bolts and not sealing well.Make sure it's sealing good or it may be causing the hesitation by letting too much air enter the box rather than just through the snorkel tube.If you don't have a manual here's one that can help.1998 Polaris Sportsman 500 Service Manual PDF Download

 

got a new carb on my 98 been running great i am thinking flywheel key is maybe bent. also grandson has a 425 expedition at what temp should the switch in the radiator turn on ? i pulled it and stuck it in a pan of water and it didnt switch on until boiling . should i get a new one I am thinking it should turn on around what 190degrees?

 

190 degree thermostat.Replace it if it's slow opening. Easy way to tell if a key has sheared and timing jumped is to pull the recoil and remove the flywheel nut. You can tell real quick if the key has sheared.