I would think that SAE 10w-30 would be fine. Cars, lawnmowers, etc... are also 4 stroke and many require the same oil. 10w - 30 says it all, it is the same weight as Strikemaster recommends, SAE approved, can't ask for much better. The bottle you received with your auger probably specifies 4-stroke because Strikemaster doesn't want someone to get confused and mix it in their fuel.
I am surprised, however, that a synthetic oil is not recommended.
Use the specified amount... too much could be hard on gaskets.
I am by no means a mechanic and someone may have a better answer for you.