Honda GC160 Engine for Troy-Bilt Power Washer

I always maintain my Troy-Bilt power washer with a Honda GC160 engine by draining the gas and letting the gas burn out in the carburetor after each use. Last month, I could not start the engine and noticed gas was coming out of the exhaust and was pooling in the air cleaner. I searched a bit and discovered it might be that the carburetor needed cleaning. I purchased and installed a new carburetor, gaskets, and hoses connected to the carburetor. I attempted to start the engine and gas was still coming of the exhaust and still pooling in the air cleaner. I've put a lot into this 16-year-old power washed including a new pump a few years ago. The machine looks new, and I don't want to part with it in place of a new one. 
 
Any ideas or suggestions of what is causing the issues I described above? 

I checked the new carburetor for leaks and when I found none, I ordered and installed a new fuel pump on the hopes that was the issue. After installation, I started the engine, and it ran for about 30 seconds and shut off. I opened the air cleaner and, again, there was the presence of gas. And I was back to gas in the exhaust. And a new issue, gas in the oil. So, it appears I perhaps bought a new carburetor, fuel pump, hoses and gaskets for naught but it did add new equipment to a 16-year-old machine. 
 
I need to research why there is gas in the air cleaner, exhaust and now in the oil. Thanks for your suggestions. I do appreciate your time and consideration.

I drained the oil, and it was indeed diluted with gasoline. I added new oil and attempted to start. The engine will not start. Again, there was gas in the exhaust and in the oil again. 
 
I have installed a new carburetor, new hoses, new gaskets, installed a new fuel pump but the issue is greater than the parts I have replaced. I have always believed it was less expensive to change parts than to go buy a new washer So for what I have paid for the parts of this repair, a new pump in 2018, I suspect I got my money's worth out of a pressure washer I bought in 2006. 
 
Hopefully, I can find someone that will be interested in taking this pressure washer and can repair it for use. Thank you for your suggestions and your time .