If the surface is edge grain and the previous finish was only wax, wiping down with mineral spirits and then sanding using progressively finer grits up to 220 or so should be pretty good preparation to refinish. Skip the soap and water treatment as it won't dissolve any wax and only complicates finishing. Before applying any finish the wood should be smooth and dry. Any staining or blotching you can see is not going to be hidden too much by a clear finish - it's sometimes possible to bleach out stains but this is tricky to do well.
If you are still getting something soaking back up after sanding down to the raw wood, it could be a prior mineral oil treatment. Mineral oil never hardens and is often used on wooden butcher blocks and countertops. Simply reapplying more would be one refinishing option. It's easy (you just apply until it is no longer absorbed) but you have to reapply it frequently. Inexpensive pure mineral oil can be found in a pharmacy (it's sold as a laxative).
Another option would be a pure tung oil finish. It would be slightly more expensive but a little more water resistant. You can get it from a woodworking or finishing supplier. Most "tung oil finishes" sold by hardware stores are not actually tung oil so check the labels carefully if you go this route. It would be applied and reapplied similarly to mineral oil.
Some "Danish oil" finishes are a blend of varnish, oil, and thinner, and others contain only thinned varnish. Generally one applies "Danish oil" in light coats such that a film is not really built up on the surface of the wood. Often wax is then applied over it. This feels nice on furniture but it is going to be less durable that a slightly thicker application of regular varnish applied with a brush or thinned and then wiped on in several coats.
The mineral oil or tung oil would be my choices for a counter that you are actually going to cut on. On the other hand if you don't plan to cut with knives directly on the counter, and if you are able to prepare the counter down to a clean, dry, smooth surface, a wiping varnish is probably the most durable and best looking option.
An angle grinder can use several "disks" that are very efficient for removing wood. You can buy what is essentially a chainsaw wrapped around a disk. Great for carving and able to throw chips around like mad, but I would NEVER bring it anywhere near a possible hit with a nail.
There are also textured carbide wheels you can put in a grinder. Also able to grind wood rapidly, and perhaps safer if it hits a nail head. Finally, you can buy a disk that is essentially layers of overlapping very coarse sandpaper. This will be less aggressive yet and the paper will wear down with use.
The other problem with using an angle grinder is it won't leave you with a flat surface easily. A grinder is a very local tool. And you want a reasonably flat surface. So if you did choose to use an angle grinder, you might still want to come back to it with a belt or disk sander to get it flat.
Of course, it is also true that other tools may not like nails either. A router for example is a BAD idea here, as that rapidly spinning carbide bit may well meet an untimely end as soon as it hits a nail. And there WILL be nails in a subfloor. If this is a sufficiently old house, they may even be great big, clunky square headed nails.
A problem with anything you use that will remove a lot of wood is the dust it creates. So make sure you use dust protection for the well being of your lungs.
Overall, my choice would be a belt or disk or drum sander designed for floor use. They are fast and efficient, and will give you a flat floor. And they will grind off any nails they hit, although nails may wear down the belts a bit more than just wood.
Best Answer
Wax is pretty hard to remove, everyone seems to agree about that, then everyone disagrees about the best way. Here is ONE way.
You can use a solvent, rags, and elbow grease to remove wax. When you apply the solvent to the wax, you get a liquid with wax dissolved in it, and when you wipe it the mix is absorbed by the rag, and thus removed. With enough passes of solvent and rag you carry away most of the wax.
For the solvent usually mineral spirits to get off as much as possible, and maybe denatured alcohol for a last pass. (The alcohol will remove the mineral spirits as well.)
For the rags, try fine steel wool or scotch pads for the first pass, then paper towels. Use a lot of paper towels. If the paper towel is dirty it's no longer removing wax it's just moving it around.
I don't recommend using a heat gun, to me that just melts the wax deeper into the wood, but it does make sense to keep the ambient temperature in the room on the warm side and keep the solvents at room temperature, not out in a cold garage or something.
When you think you've removed the wax, let that last pass of alcohol dry then spray the surface with water to test. If the water beads up, try to remove more wax. (Note that some naturally oily woods may bead up even with the oil removed so this isn't a perfect test.)