It depends on what it is.... By the sound of it it is
old oxidized preservative oil --
You can apply a little bit of vegetable oil and let
it rest for an hour then wipe off. A couple applications
may be needed.
WD40 is a good goo remover.
If it is a spray on lacquer removal will be
harder but if it is hard to remove it will
not hurt the strop.
You can strop on newsprint for a while
and just toss the top layer of paper.
Try the obvious safe bets -- hot water and
shave soap, mineral oil, wipe with tissue....