I agree with R42Pilot. If you are using so much oil it drips, you are using too much!

As for me, I wash my chain in kerosene and brush it clean with a brass brisle brush. I let it dry outside in the sun. I then lube it with Mobil 1 oil on each plate and roller. I run the chain backward several times letting it set between times. I then wipe the outside of the chain to get it reasonably dry. I wipe it down after each ride and re-lube as I need to. BTW it never drips.