Nice looking piece there. It's good to see it being put back to good use.
I think Cliff and Scott Vt. have it about right. This looks like a 1920's factory piece that was either fumed with ammonia or stained then shellacked.
What I would recommend is what Cliff said - clean the piece with mineral spirits or Naptha to dissolve the wax and accumulated crud. Sand lightly with 220 or 320 sandpaper to create a "tooth". Be careful not to cut through the old finish and expose any traw oak - especially on the sharp conrners. It's easy to cut through when sanding, even with 320.
Go over the piece with a tack cloth (at paint stores) after every sanding, and use a new one each time to remove all dust and grit.
Then give it a coat or two of clear shellac - remember shellac is an alcohol based finish, so it dries fast - you need to keep a continuous wet edge as you go over the top and the rest of the piece. Shellac is also pretty thin so it is easy to get drips and sags on the vertical surfaces. Clear shellac won't change the color, you could also use a mixture of clear and orange shellac if you want to add a little warmth to the piece.
Sand the shellac lightly with 320 again to give something for the poly to stick to. I've had good luck with teak kitchen counters with two coats of water based gloss poly, and one or two coats of satin. The water based poly dries in an hour or two, and doesn't smell as bad. I've been using it for about 10 years and haven't had any problems. If you want to be really safe you can use spar varnish or marine varnish which is designed for sailboat wood work - that's as waterproof as you get without going to the plastic look of epoxy, but dries slowly, so you have to have the piece in a dust free environment for at least 24hours after each coat.
I would also recommend finishing the counter top portion before you install the sink, and be sure to finish all the end grain from where the hole for the sink is cut. This will minimize water wicking into the wood and swelling, splitting over time. It also might make sense to remove the top and put a couple coats of shellac then one of poly on the underside of the top. As a sink base it will be in a wet environment and the unfinished underside can absorb moisture and swell which will cup / warp the counter surface.
You can usually find clear and orange shellac at the big box stores (HD & Lowes), but be careful - shellac has a short shelf life. There will be a production date on the can, don't buy it if it is more than six months old.
Good Luck!
Rob H