cbt
With it being oil, depending on fabric of course id try either solvents, you can disolve a good citrus gel with hot water and your pre spray which might do the trick or Grease Break from Hydramaster which is a liquid pre spray addatiive might do the trick also, the best would be pog but since the cancer warning I dont like using it,
But id try a chair first before quoting or you could be in touble.
The oil being mainly massage oil is propably organic so would prob come out with a good enzyme pre spray
but id be carefull of the wood if using enzymes or solvents might damage it and would need a lot of vasiline and time
but sholdent take more than a couple of hours
good luck James