I had this same problem a couple of weeks ago on a dining table we received from a relative. The top was partially discolored (it looked like the original protective covering had been partially worn away). I was hesitant about sanding it but I was refinishing a couple of smaller tables at the same time, so I figured what the heck. I got some fine grit sandpaper and lightly started sanding a small section, just to see what would happen. The old finish came off pretty easily and it was kind of gummy little balls (I had to change paper often). I went ahead and sanded the whole surface and then applied a polyurethane clear coat (3 coats). The table looks really good now. I think as long as there is no stain in your table, you should be able to sand it down no problem.

I use these (professionally) and have never had a problem removing a water blush in just a few minutes. You can also usually find them at Ace Hardware, Lowe's and Bed, Bath & Beyond in their cleaning / furniture care product aisle. In my experience, rarely would you need to strip and refinish unless the finish is blistered and peeling off (I can't tell from the photo) Likewise, you may need to buff out the whole top to even the sheen. The cloth will also remove light scuffing. Clean up the residual oil with an emulsion furniture polish Here is a link that might be useful: water ring removal cloth

Scrubbing with a wire brush, in the direction of the grain, doesn't leave oval sander marks. It will make the grain a bit deeper. There is a brand of waterproofer that claims to not have a yellow tint. It will darken the wood slightly (as if it's wet). I don't remember the name.

Wipe some mineral spirits on it and see what it looks like before you go fooling with stain. If it looks good like that, you can just apply some brushing lacquer. Watco and Deft are two common brands. Lacquer is what is on there now if it's the factory finish and will bond perfectly with it. Believe it or not, not all clear finishes are poly just because that's what jams the shelves at the home centers. If it does not look good wit the mineral spirits, get a chemical stripper and take it all off. Sanding off an old finish is a poor way to go. It will not get it all off and if the table top is veneer (and it looks like this is because of the different grain directions and edge banding), you risk sanding through the veneer and ruining it. Stripping is messy, but effective, less risky and it's over without gumming up 8 sheets of sandpaper. But if it's ever had Pledge on it, it will likely "Fish-eye" The cure for this is to put on a coat or two of dewaxed shellac (SealCoat by Zinsser), then apply whatever finish you wish.