Mechanical cable-actuated disc brakes started working really badly
My guess would be the cable is old. The inner cable begins to seize or bind with the outer cable. This could be caused by corrosion caused by water ingress over time or dirt ingress over time. 

The binding basically causes more friction along the line of the cable - eventually preventing a smooth return to the "Off" position on the brake lever. 

You can do a "bodge" and that would be to squirt something like WD40 down the cable line to free it up. But this is only a temporary fix.
The proper fix is to install some quality pre-lubed cables which are also weather sealed.

Incidentally, pads contaminated with oil can be cleaned by removing the pads and heating the pads over a flame to burn off the oil.