You should use 2 stroke oil with the fuel and gearbox oil in the gearbox. Email your engine details to a Suzuki dealer to get correct spec of gearbox oil .
Definitely not on using ordinary engine oil in the fuel of a modern 2 stroke.
2 stroke oil is designed to lubricate crank pins when mixed with a fuel mist, then burn cleanly with minimum residue passed to the environment, with low ash to prevent coking up the engine top end. 20W50 is not designed to do any of the above.
If you use the wrong 2 stroke oil - say cheap stuff designed for air cooled lawnmowers, this is designed to burn off at the higher temeratures that air cooled engines achieve.
The correct oil is designed for the lower temperatures of a water cooled engine, and to have minimum impact on the environment.
2-stroke oil. TCW-III is latest spec. Over the years I have found Quicksilver and OMC to be the cleanest burning.
Last winter I had the head off my Johnson 4 (after 16 years of use) and there was no carbon build up worth bothering about. The plugs have never - ever needed cleaning. More recently this has been run almost exclusivly on OMC oil (Johnson / Evinrude).