Hey there,
if I understood right, it seems to me that your engine is leaking. While driving the wind will spread the oil all over your transmission and underneath the car. Transmissions usually leak at the front and rear shafts.
It´s usually the sheet metal valve cover with the cork gasket. The sheet metal bends at the fastening points and thereby looses pressure on the gasket (which additionally hardens due to heat and time). A well known problem. Volvo had a little improvement with some sort of special washer under the fastening screws.
The better solution would be an aluminium cover with silicone gasket. In the past it was sold as "R-Sport" part.

Hope my english is not too rusty and you understand what I mean.

Kind regards,
Zig (riding old Volvos PV444 to 1800ES since 1966)