How to get rid of spilled olive oil on teak table?
It could go rancid and smell for sure since it's a vegetable oil.  It's definitely not used for finishing things like cutting boards for this very reason.

Soap and water are useful in getting oil off of things that are sealed, but if it's discolored the table I'm guessing it's not very well protected.  That makes the problem difficult since any kind of oil seeps deeply into wood fibers.  I'm not sure how far oil penetrates into Teak since it's a naturally oily wood in the first place.

If you do manage to get it cleaned up (which probably involves sanding and refinishing at the very least), it might be worthwhile to build a nice protective finish next time.

Check out this post for more information:
How do I fix up an unfinished, oil-stained pine table?