To clean the dirt and crap out of well weathered teak, I used a strong solution of water and TSP (TriSodiumPhosphat).
Just mix up a batch by disolving half a cup of TSP in 4 cups of water, then apply liberally to the teak.. Let it soak for 10 minutes, then use a soft bristle brush to extract the dirt out of the wood. Rinse with fresh water, and you''ll have some clean teak to work with (apply your favorite teak oil etc.)
I had the luxury of removing most of the cabinets, drawers, rails from the boat and applying the TSP to the woodwork in the garage.. Just be careful not to spill and/or be ready to quickly rinse a spill area if/as required..
After cleaning the teak either by sanding or using one of the commercial two part cleaners I have tried several teak oils. All looked beautiful at first but even with repeated regular applications, ended up looking pretty bad by season end. A few years ago I switched to Cetol-marine. This pigments the teak a little and leaves a hard varnish like finish but it is durable and lasts. I typically get 2 or 3 seasons now before I hae to recoat.
I use Bristol 2 part urethane. It has saved my life on teak maintenance. It looks as good or better than varnish, easier to build coats, dries faster, levels easier, and lasts for over a year here in Florida. I now apply two coats of Nu Finish car wax (not really a wax) and it lasts even longer before recoating. Great stuff.