Stabilizer (and I've only used "Sta-bil") keeps gas from going bad by adding a lot of alcohols and varnish strippers to the mix. The alcohols (like "HEAT") trap/mix with the moisture, and the other hydrocarbons keep varnishes from building up in the carbs/FI. A serious petro-chemical engineer could be a lot more specific (accurate?), but that's the gist.
As for 2-strokes, I've never popped in additives under the cheapskate assumption that the oil-gas mix would solve all problems during the winter. That being said, my 2-strokes consit of a weedeater and a couple of $500 scooters [:)] YMMV.
Always do an oil change...there's so little oil, it's worth the extra hassle just to be able to say to oneself that "I did all I could". Except for 2-strokes, of course [:)] If you have a 2-stroke, there's probably no good way to "change" oil. That's the way it's on my scooters, anyway.
I've been running my Nighthawk (4-stroke) on winter-stabilized gas for a little while. I do add new gas every gallon or so, so take from that what you will.