Have you checked to see if it is leaking around the oil fill plug? I had a Stihl 044 that was leaking oil the way you described. I assumed it was coming from the oil mechanisms but it took the dealer to point out that it was coming from the fill plug. Instead of closing it hand tight I started tightening it with the bar wrench and the leak stopped. The thing is when they leak like that and become an oily mess, it can be hard to tell where the oil is coming from and he thin film of oil dripping down the side of the body is not always easy to see.
I had a Husky 357XP that also leaked oil like yours after it had a lot of hours on it but it was not leaking from the plug. It was coming from somewhere under the clutch cover. I eventually traded the saw in after some other things broke so I never did look into the leak. The fuel plug leaked though and it uses the same type of plug that the oil tank uses so I would imagine the oil plug could leak too. My Husky 254 leaked oil the same way from under the clutch cover when it got some age on it. I don’t have anything useful to say about that but checking the plug is a place to start.