Take your finger and dip it in the oily mess and smell it.
Does it smell like gear lube smells (if you forgot what that stuff smell like, buy a tube and smell it)
My guess is that the guy used too much 2 stroke mix (hey, more is always better right>>???) and now that you are storing the unit upright, it drains the engine well and over time it will drip black 2 stroke oil out the vent which is designed to be sure no water is trapped inside the foot so it won't freeze.
But I am no outboard mechanic and maybe the hole you talk about is something different. I don't believe there is any venting hole to the drive gear area...and it should be sealed up with solid bearing seals at both the top of the drive shaft and in front of the prop.