You degauss a screen using a degaussing wand, or some monitors actually have a seperate degauss feature which you can initiate whenever you want. This is to cure problems where a strong magnetic field has been placed close to the CRT and produced purity errors, or if the monitor has been moved while it was switched on. You'd know all about it if you had purity errors - the whole screen would be a mix of deep purples and greens.
Regarding the overgunning thing, I don't think that's your problem. It looks from the picture as if you might have too much green in it, but I think it's just the way the picture has come out. Either way you definately have a problem seperate to that with the distortion in the picture, so concentrate on that first.
Distortion like that you describe can be caused by a problem in the switch mode power supply, or perhaps in the line output stage. I've not had many of these types of problems, but normally it's to do with a capacitor which isn't behaving itself anymore. It's not the type of problem that a novice to TV repair can really attempt, unless the component in question is waving it's hand in the air shouting "look at me, I'm faulty." Capacitors can sometimes give you this indication; they'll either bulge at the top or weep at the bottom, leaving a mess of toxic chemicals in their general area on the board. You could try taking the cover off and giving the board a really good visual inspection for these kinds of things.
BE CAREFUL because even when the TV is off, there are potentially dangerous high voltage areas on the board.
Brian