Recently changed the oil, oil filter, and air filter in my polaris phoenix 200. I noticed lots of smoke from the exhaust a couple of days later. I went to check the oil and air filter. When checking the air filter, it was saturated in oil with oil in the filter case. I drained the oil again but hardly any oil came out. What would be the cause?

SOURCE: Water build up in the starter & Reqoil case of my Polaris ATV

Your drain plugs should be visable, if they exist, on the lowest point of the body of the device. If you can't readily see them, consider drying out the entire unit with a hair dryer and a little patience in drying the entire unit. From then on, I would consider evaluating the depth of water before entering. After all, the unit may not be amphibious, which sounds like your intended use!
Also, the battery may be affected by the extreme cold, as they often are, leaving a different approach to this problem. Good Luck!

SOURCE: Check 4 wheel drive light appears after 4x4 is engaged.

transfer case make grinding in shake when in 4 wheel

SOURCE: check engine light on

It can be.
You must go to a mechanic with the diagnostic machine to check if there's something more causing that. But you can precheck by yourself, remove the battery cables for a few minutes and check if the llight is still on, this should clear the memory, if not, it means there's something more.

SOURCE: Gas entered the exhaust system and then oil reservoir. I got the gas out exhaust change oil. Mower runs but in question is gas still entering both places.

the little solenoid on the bottom of your carb is letting gas flow while it is not runnung.therfore gas gets into your oil.About an 80.00 part..or you could just turn your gas valve off when your done mowing.but still you would have to eventually replace that part.hope this helps

SOURCE: Oil in my air filter case

The rubber grommet on the top of the Rocker cover (valve cover) has a rubber grommet at the back of it may be plugged. You can either replace it or open it up with an awl. it all depends on its condition burnt and melted. If the engine has high mileage, I suggest checking the EGR for clogging and the engine compression. You can try heavy body oil and an engine oil treatment to help reduce the blow by or compression loss on this worn engine.