I have already oiled the majority of the sofa table, but I did not oil the top because I wanted to completely refinish the top. I don't really have much experience doing this, but that doesn't usually stop me from trying.
So I took the cabinet scraper to the top only to find that the top isn't level. Apparently the pieces were sanded separately then glued together, because the joints aren't level. The cabinet scraper couldn't get it all because it kept riding up on the higher pieces so the blade would stop cutting. If I kept going to cut down the higher piece I would have torn out the far edge. Having been stopped at this point with the cabinet scraper I switched to a card scraper to get the majority of the rest of the finish off. There were some spots that I just could get at, though, at least not without removing a lot of material. An example is shown below - at the joints there is finish left, and it's ugly. I wiped the wood with alcohol to make it more visible.
I asked for opinions on the Canadian Woodworking finishing forum and decided to just sand the bejeebers out of the joints to level them, then blend them in. It won't be really flat, but it will be closer than it was.
After more scraping, and sanding, I ended up with this:
Now I let it sit over night. I wanted all of the dust to settle before I started doing any finishing.
The next step will be the seal the surface and fill the pores before staining and clear-coating.