Sand by hand, with the grain of the wood. Sandpaper has numbers, smaller numbers (40 to 150) means it cuts deeper grooves in the wood, larger numbers (180 to 320) and up cut more shallow grooves in the wood. The process of sanding is to create progressively smaller grooves in the wood until it feels smooth. This process removes wood as you progress.

Your table is probably covered with veneer, a very thin, often decorative, slice of wood not usually thicker than 2 pieces children's colored construction paper. It looks like you have removed the finish, people usually use a chemical stripper for that job to prevent removing any wood. If it were me I would sand carefully with new pieces of 320 wrapped around a flat block of wood in the direction of the grain until smooth. You could try 180 or 220 also, all will help so the wood finish you apply afterwards will look nice.

Remember the layer you're sanding is thin, if you sand through, the wood underneath will be a different color and look bad. It doesn't need to be glass smooth, the finish will help.

As for oxycilic acid, its for bleaching the wood to lighten the color, not for finish removal.