The carburetor flooded resulting in excess gas to wash down the cylinder walls and contaminate the motor oil, which you've already noticed. Changing the oil will solve that problem and no, the motor won't blow up in your face. Gas in the oil is a common symptom with carburetors that flood. The fix for the oil is to just change it. The carburetor flooding, however, is another story.
In my Craftsman 22HP garden tractor, the carburetor flooding was caused by deposits in the float bowl that caused the float to stay open. Rebuilding the carburetor (or replacement -- overkill) will solve the problem. However, keep in mind that whatever is causing the deposits in the fuel bowl might cause the problem to re-occur. In my case, it is due to a gas tank that caught rain water one season leaving gunk that keeps contaminating the fuel system.
Don't be intimidated by the prospects of rebuilding the carburetor. It is a very simple system and rebuilding is simply a matter of disassembling it, cleaning with carburetor cleaner, blowing out passages with compressed air and reassembling. It will make the tractor run like new.
Oh, one WARNING: Another user recommended soaking the entire carburetor in carburetor cleaner, then blowing out the passages. DO NOT DO THIS without first disassembling the carburetor and removing all plastic, rubber and foam peices. Carburetor cleaner is extremely potent and WILL dissolve or otherwise ruin these parts. Many floats are made of plastic or foam. Your carburetor rebuild kit probably doesn't come with replacements.
