I think that after you change the oil & oil filter it'd be a very good thing to check to see if your fuel tank/tanks are clogged w/ "stuff"
...,you may have to completely flush them out until you're sure there is no more rust or dirt,water,etc. in them..,you may have to re-line the inside of the tank/tanks if it's real rusty.
First thing to do is drain the carb. bowls & catch what fuel comes out of them in a white colored plastic spray can cap..,that'll give you a hint as to what's in the fuel tanks.... I'm not sure that this is your problem,but I know that if it is, it'll cause your carb. float valves to stick(from small particles & chunks of rust) which'll overflow the carbs.
The other thing that'd be good is to remove the carbs & go through them,check the condition of the float valves/needles & seats & clean/blow those carbs passages out real good.Does your model VT500 have an electric fuel pump(if you do,the fuel pump needs flushing out along w/ replacing your inline Honda fuel filter also) & a sub(under seat type)fuel tank ?,you know,a main top fuel tank & a small frame mounted tank ? Those small frame mounted tanks can Really get lots of rust/water,etc. in them over time.The other thing that would be good is to see if your fuel valve/petcock is sealing well when you turn it to the "off" postion;it makes a lot of a difference especially if it only has one (upper) top fuel tank & it is a gravity feed only system.
Let us know what you find in those carb bowls