I once treated this type of furniture that had been left out in all weathers for some years. I used a detail sander for all the fiddly bits and an orbital sander everywhere that it fitted in/on, including slats that I removed by unscrewing them. Before all of that I used plain soapy water and scrubbed the worst bits with a hard brush but wiped the excess water off straight away so as not to let it soak in. I made certain every surface was cleaned and sanded without rounding (hence the equipment, abraisive in hand is not flat). I actually used a chisel and sharp pen knife to get into the corners and carefully scraped the last bits. Once oiled it looked (and still looks) literally like new - this is because teak takes a very long time to spoil more than just superfically. To assess how far yours has gone, carefully scrape at the worst bit with a sharp pen knife or similar.