Going to disagree with a lot of what's been said, not that it's wrong just that it could be a different solution needed.
Cables, ok to oil them IF they are aftermarket, most don't have any liner fitted to the inner cable, if they are genuine it's ok to use silicon oil but not mineral oil etc. The liner or sheath on the inner is teflon and it reacts to mineral oil by swelling but is fine with silicon.
On the butterfly system on the carbs, where the cables connect to just release the nuts holding the cables tight, start with the bottom or push cable, a single nut usually holding it to the bracket, release and slide cable out, disconnect nipple from butterfly and put to one side, same for the top or pull cable. Very easy really.
Main jet, as said it's held in place by a small oring so should just pull down and out, however most people tend to grab them with pliers and mark them, wrap it in a cloth before trying that. I don't think it's corroded, when petrol evaporates, as it does over time, it leaves a tar like residue, that's what is coating the jet, once that comes off you'll most likely find it's still looking ok. Hopefully. Boil all the brass in soapy water and see if that helps. The drain screws will be blocked, get some thin wire and have a dabble in there to see if you can get it all out. Pilot jets may look ok but look up them against strong sunlight to check all the crap is out, you should see what looks to be a small spiders web inside the jet, it's an optical illusion but usually means it's clean.
Once the cables are off and the clips are all loose the carbs will pull out, a lot of people just pop off the rear rubbers to get the room for them to go backwards, not saying that's a good idea or a bad idea, it works but it can be a little awkward getting them back into place. It's a lot easier than undoing the airbox for instance, your choice. If they are split anyway I'd certainly do it that way.
As for Honda carb oring kits, Bryan is right and wrong, he's right they don't have enough rings for the T pieces on the fuel lines, however the kit is for 1 carb only so 1 carb only uses 2 rings not 4. Buy 2 kits and you have enough to do one T piece, buy 4 and you have enough for everything. The problem being that it's likely but not certain the orings will be nitrile not Viton and so you may have issues using fuel with ethanol in it. The plus side is that the rings are the exact size specified by Honda and AFAIK all aftermarket ring kits are not, the sizes needed are unique to Honda and unless you get them specially made to order they'll be a compromise of the nearest size commonly available. Hence why most orings for the float bowl leave a little extra and you have to glue the ring in place (500/550).
Pulling the carb bank apart can look daunting but just have 5 boxes ready, I use plastic takeaway containers with lids, mark 1 to 4 and one marked body and keep everything separate. How's the throttle linkage bar looking? rusty?
