No there isn't any need to turn them off, and yes they can be turned off by turning off the air flow to them (i.e. either though a valve or by turning off your pump

).
As to them giving off larger bubbles, that is due to the clogging of the various pours in them that I mentioned. What happens is that as parts of the pours (think of them as very tiny pipes) get clogged up, but only one section and not the entire length. So you start to get air forced into part of the pour that isn't clogged but it doesn't have anywhere to go. So the air looks for another way out and moves to a pour that is clear. By doing this you will get a pressure build up inside parts of the stone. The pressure will build up but since it's not a completely clogged stone, it will just rush out of another hole. This "rushing" of air causes the pressure in the stone to actually become lessened for a short while and that air that was sitting in the clogged pipe will now actually get sucked out by the vacuum effect. So for that moment in time you will get larger bubbles being shoved out of the stone, and then the process starts over again. And since these pours are really, really small, it's happening quick enough to look like it's always sending up larger bubbles.
So what does all that ramble mean (man I can go on can't I :

)? It means that it's time to change your airstone. You can leave it if you like the effect of the larger bubbles for a little while, but eventually it "could" start to create back pressure in the stone and that can hurt your pump (I say "could" because we use valves that create the same pressure all the time and our pumps just keep pushing air, so I'm not sure I actually believe that it would ever actually cause damage). You could try to clean it, but considering
they only cost about 50 cents each, it's just not worth it. Though I have heard good things about
the silica airstones in that they don't clog as easily, but I've never used them so I can't speak from personal experience.