Teak furniture care/repair advice

Good morning...first post on the forum...seems like a good helpful place to have! I am new to the DIY home improvement stuff...

so, I just purchased a pretty nice set of 4 or 5-year old teak patio furniture. It looks pretty good, and I got a pretty decent price on it. However, they claimed they oiled it every year, but it sure doesn't look like it in some areas.

I live in Denver, CO which is notoriously dry, so that may have helped this look not the best it could.

The chairs look in good condition, still straight and strudy. However, the table could use a bit of work. The table top edges have a slight bit of warpage (which makes me think it may not be true teak, or it's just their minimal care that helped cause it), but it's not bad considering the price I paid.

What can I do to alleviate this problem any further? I'm debating on pulling every piece apart to sand every crevice, then oil it up rather than just clean and oil with it all together. If I oil a few times over, will it help any or will one coat be enough for now? I will definitely be oiling periodicially throughout the year.

How about some kind of protective coating? I know the beauty of teak is to keep it natural, but I'm more into keeping this a sturdy and realiable table.

I'm really just looking on advice to stop the deterioration of this as quickly as possible!

Thanks a lot, and I appreciate the help!

-Nick