Waxed pine dining room table

Grease sinks into the wood. You will have to start over. Sand, stain, then put a coat of clear poly on it to protect.

Try rubbing coconut oil in with a microfiber towel

Rose is right. Then use placemats and coasters to prevent future damage.

You might consider sanding it to remove all stains, finishes, etc...then coat it with polycrylic or something similar to protect it.

http://www.ehow.com/how_7680674_remove-oil-stains-wooden-table.html

When I do waxed furniture finish, I first apply a coat of spar varnish, then use paste wax. So I would strip all the wax off, varnish, then wax. I would try some ammonia and water, and 000 steel wool.