Clean Teak Moller Chairs  

I love this stuff. I don't...
I love this stuff. I don't see a "teak" per se, but I've used dark walnut on any dark wood. It's more about matching the color methinks.
http://www.howardproducts.com/restora.htm

im a huge fan of Old English...
im a huge fan of Old English Lemon oil...the untinted type...very quick and uninvasive...removes old wax which tends to leave finished wood dull. doesnt have a super strong scent either...it can be bought at just about any hardware store for chaep and a little goes a LONG way...as far as excess oil,just wipe it off. doesnt really leave a film

A good rubdown
The nice thing about teak is its deep, rich grain and color and the natural waxy resins it contains that help to provide its legendary durability in harsh environments. For indoor use, it really needs very little care at all beyond keeping it out of direct sun to prevent excessive dying and/or bleaching and the occasional cleaning.
You could wash them with a plain soap and water, but I would start by giving your chairs a good vacuuming and then the wood parts a good rubbing with a cotton rag dampened, not saturated, with white spirits working outdoors or in a well-ventilated space wearing gloves. This should remove any grime and most surface build-up of previous oil or wax treatments. Take care to keep solvents away from any leather, vinyl or textiles.
After 24 hrs, or so, of drying, most or all of the solvent odor should be dissipated and close inspection should reveal the need for any further action, such as treatment of disfiguring stains. At this point, there is really nothing more at all necessary unless you wish to sand any rough areas or apply an oil finish and/or wax to restore some luster or sheen. Any good "Danish" oil finish like Watco should dry completely in a couple of days if applied in accordance with the directions supplied, though they tend to darken wood a bit. Paste-waxing, either instead of or after, oiling is also a good option for imparting a smart, protective, low-gloss glow.

just curious....
because it seems to work well....is there any detriment in using old english??i havent noticed anything, seems to do exactly what im looking for..but im not super savvy when it comes to that sorta game....

Probably nothing wrong with it.
The MSDS lists petroleum distillates as 90-100 percent of Old English Lemon Oil ingredients. That means up to ten percent is the unknown proprietary formula. As you mentioned, it probably doesn't leave much, if anything, behind. I would consider it a relatively benign, pleasantly perfumed cleaning solvent and not a "protectant" as marketed.

Is there anything wrong in us...
Is there anything wrong in using Murphy's Oil Soap straight up, no water added? I've used it in the past to clean grimy teak and it's amazing how easily the crud comes off with it. I've also used white spirits and even turpentine, which I think is one of the few things that dissolves wax, and neither of them got the actual DIRT off as well as the Murphy's. I'm talking about the grime that builds up on the chair arms and back where a billion grimy hands have touched the wood over decades.
I rinse the soap residue off with as little water as possible, dry the wood immediately, and then let it air dry for a day or two before oiling.

Old-fashion soap flakes and water
would probably work nearly as well and, while not easier, would certainly be cheaper and you'd know exactly what you are putting on your heirlooms.
To help maintain integrity and value, I'm a big fan of Les Ismore and I'm, perhaps overly, suspicious of most "snake oil" products that promise shortcuts to superior results.