The stains could be water drips, it's hard to tell without a photo.
Don't use oils on teak - it's naturally oily and more oil just attracts dirt. It looks good for a short time, then yuck.
Sand lightly, wipe with acetone, and finish with Minwax satin or semi-gloss wipe-on urethane. I used Minwax gloss spar urethane on high wear areas like handholds. The finish will hold up forever and only needs a water wipedown from time to time. I used the gloss on my sole as well.