Do 1 at a time. Your bike is running, so I suggest not to separate the carbs from each other (the fuel lines between carbs don't leak, right?). THAT would make it a lot harder but still not brain surgery either.
Just remove all bits, jets, emulsion tubes, screws, etc. and blow carb cleaner/compressed air through all the passages. Pay extra attention to the emulsion tubes, I think there's 1 for pilot and 1 for mains, they have tiny holes through them and they need to be clear. Never use anything harder than brass to clean them or you'll enlarge the holes those things are easily dinged. Your bike looks more like it needs tuning than actual cleaning, as seen from this end of the internet of course, so...
Try
this for rubber bits, the "gasket kit".
If you're nervous now, wait until you start taking apart that motor