if you can smell gas in the crankcase oil via the dipstick, DON'T RUN that engine until you can get that bad oil drained and refilled with good oil. M/W, pick up an inexpensive inline fuel shutoff valve - install and use it to shut off fuel to the engine's carb every time you shut it down.
Most likely the carb float needle valve is not sealing right and is letting raw fuel dribble right thru the carb into yer cankcase, diluting the oil... bad news.

A Briggs 80202 has a Pulsa-Jet carb, so a fuel shut-off doesn't make any sense because the tank is below the carb. Also, there is no float needle valve. Previous poster may have confused with 803XX which is float style Flo-Jet carb.

You should look at choke operation. You may be over-choking which would pull raw gasoline into the carb. From there it could go into intake and then wash past rings, or it could run down the breather tube into crankcase.

However, both Vacu-Jet and Pulsa-Jet carbs generally do not pull up excessive amounts of gasoline. They rely on vacuum to list gas from the tank. About the only way you can really suck up a lot of gas is to place palm of hand over the air intake with air cleaner removed while cranking or running.

understand the pulsa-jet thing.. but - if there's oil diluted by gas in the crankcase - it still needs to be changed before that engine is run again.