Skovmand & Andersen table  

It is veneer, so you need to be very careful sanding. You might try remove the old oil with strongly mixed and very hot murphy's oil soap. Then use oxalic acid for dark water rings. Then I suppose you could gently sand scratches (I use a card scraper for this, which is much more effective, and much safer, but it isn't probably for your first attempt). Then apply teak oil to the surfaces. It is likely the main surface will not match the leaves, especially the dark lines in the leaves.

Thanks for the tips! I kind of figured the surface would not match the leaves again but hopefully I can get it a little closer in colour.

You can custom tint later coats of oil with just a bit of artist's oil paint. It basically makes a custom tinted danish oil. Good for color correction/matching.

I was going to ask about that. I read in another of the threads about tinting the oil but couldn't remember where.
Would turpentine serve the same purpose as murphy's oil soap for removing the old oil? Also, are there teak oils I should avoid? I have a can of Minwax Teak Oil somewhere but have no idea if it is a good one or not.
I also got 5 chairs with the table, nothing fancy but made in Denmark and they match the table. New to this but I thought $160 for everything was pretty darn good!

Is this the technique you use Leif? Has anyone used this product?
Just trying to get all my ducks in a row before I attempt the table : )
http://www.thomaspenrose.com/diy_stains01.htm

Nice buy! We had a beautiful Skovmand & Andersen table last year. Your set was a steal!

That technique will work. I use oxalic acid crystal mixed in water. You may not need to use oxalic acid at all. The first step is to remove the existing oil finish and see what you have then.
I doNot think turpentine is going to work well to remove the old oil finish, but you could try it and report back.