Some how the air conditioner vents on the passanger side of the car became jammed and cannot move left to right and hence are locked in a near closed position. How can these be un jammed without causing further damage
The first thing I'd try is to use a flat bladed screwdriver to gently pry the vent slats back to the open position. Chances are you'll have a bit of a pop and they'll move again. If you exercise them back and forth regularly they'll likely be fine without any further work. Cleaning them would be a good step, an old toothbrush may fit, otherwise some other kind of thin brush can be used to brush the joints clean of sticky dust.
However, if they still stick you'll want to lubricate them. I'm a fan of silicone lube for plastics like this as it won't cause discoloration, but you have to be careful how you apply it or it could get all over and make a mess. A cotton swab is pretty effective at getting into spots like that.
Those vents probably pop out, if you have plastic body repair tools you could use a wide, flat pry tool to work around it and pry it out of the car. You could then wash it, dry it and lubricate it much easier. If you don't have the right type of tools you can improvise them, just don't use sharp metals or you'll damage the finish of your dash.