After riding for awhile and I turn off the bike I get drips of oil coming out of the air cleaner .

the breather hose is the means of allowing the compression by pass gasses to not build up pressure in the sump and it exits into the air inlet system near the air cleaner
for oil to be dripping there indicates
1--excessive oil in the sump
2-- worn rings allowing excessive blow by and boiling the sump oil
3-- incorrect oil used in the sump ( too thin) try a 30w -50 grade

DETERMINE WHERE THE OIL IS COMING FROM (very easy on that bike). If it is dripping down from the air cleaner assembly, check to see that the oiler hole for your air cleaner isn't overproducing (common problem and easily dealt with). All Sportys from that era mark their spot to some extent due to the breather/oiler. Just make sure that it is not a crankcase leak. If it is a crankcase leak, simply replace the offending gasket or seal.

Also, check to be sure that it is not a brake fluid leak (less common but VERY dangerous for you), and check the seals around the shifter shaft to make sure they're not compromised.

this means you have to keep checking your oil more often, try this clean a big portion around the oil dripping make sure is clean when you finish you can turn the moped on give it a little gas,right away check for the oil leak once you spot it that would be your starting point.
good luck!

check your fill cap, the seal is know to wear out after time i have seen it on a lot of bmw's drain a little of the oil the right level there is a chance that the case breather pushed some oil into the air box.
clean it up go and take a ride see what happens.
Let me know what happens
M.Woodring

Regrettably, a small oil leak from the air cleaner assembly is "normal". This is because the EPA requires all crankcase emissions to be routed to the intake system so that it can be burned in the engine. The result is that oil mist in the crankcase vented condenses in the air cleaner and eventually drips out.

The crankcase vent for your Sporty is in the heads. If you noticed, there are two large bolts that are hollow holding the air filter backing plate on. The crankcase vents into the air cleaner assembly through these two bolts. There is an "unbrella valve" in the rocker box center section that allows the air to flow one way but not the other. There are baffles in this area to keep the oil mist to a minimum but still there is some in the air coming out of the engine.

There are a few kits available on the aftermarket for re-routing this crankcase vent. You can direct the exit anywhere you wish using one of these kits. Most people just route the hose down and exit it under the bike just in front of the rear wheel.

When adding oil to your bike, only add the oil when the engine is hot. On your dipstick, you have two marks. The upper mark represents "FULL HOT" while the lower mark represents 'FULL COLD", Do not overfill. Check the level with the bike on the side stand.

Good Luck
steve

All Harleys after the year 1992 will have some engine oil carry over visible in the air cleaner though there is a diffrence between excessive and normal although if you get on your bike and travel down the highway at a constant 80+ MPH you will find that you get more carry over to the air cleaner then you would normally riding at lower speeds and this is simply cause you are running the engine harder and therefore you will see more carry over at the air cleaner. Now to be sure, make sure your bike is sitting on level pavement and in the case of a Softtail model it should also be upright and level pull the dipstick from the oil tank and wipe it clean, reinsert fully into the oil tank and remove it again and look to see if your oil level is roughly halfway between the check marks on the dipstick. If so then yes your oil level is good. I would now remove the air cleaner cover and wash any excess oil out of it and if your running a stock air filter and you have had a oil carry over issue for awhile now, then replace the air filter, reinstall the air cleaner cover and go ride the bike for around 50 miles and by ride the bike I mean go ride it like in town and on the highway without being abusive to it or excessive speeds(70 mph). Then remove your air cleaner cover again after your test ride and look to see if you have any oil carry over in the air cleaner. if so let me know and we can go into further detail.

Relax...... Harley's all vent oil thru the air cleaner, actually, S & S does to, except they put a overflow valve so it drips on the road rather than the engine. Various little things can cause the oil flow to increase, and yes, over filling, over heating, and sometime, just running balls out for awhile.

Its normal, and shouldnt cause any problems more serious than oil mist on yer engine ( and sometimes passenger)

Replace the Oil Blow-By Stopper

Check the compression. Pressure getting past the rings can cause the problem. Does the bike burn any oil when you ride? If it does the rings are suspect....... Okay, you have oil > is it the right oil? The prior owner may have put something stupid like 5w30 oil in the crankcase. Do an oil change and put in the heaviest oil Suzuki says is proper. If extra emission stuff is on the engine the dealer should be able to identify the items and you or they could remove or bypass them. Are they contributing to the problem... who knows. Kind of a shot in the dark on that part of the equation.