With the generator bogging down, I don't think the problem is with the oil pressure. That should cause it to just die. Bogging down does sound like the carburetor.
Gasoline is cheap. To be sure you don't have water in the gas, drain the tanks and replace all of the gasoline.
I agree with the Seafoam recommendation. My Honda will never see a drop of gasoline that doesn't have Seafoam in it. (It will also never see a drop of gasoline with ethanol in it if I can find a station that sells "recreational gasoline.")
Seafoam does work. I had some lawn equipment that almost wouldn't run because the carbs were gummed up so badly. I ran them a season on double concentration Seafoam, starting them every day or two for 10 minutes. That was long enough to flush out the crud that had dissolved overnight, and put fresh Seafoam in the carb. By the end of the season, all of those tools were running like they did when brand new. Now, I put Seafoam in the gasoline container before going to the station to buy (ethanol free) gasoline.
