some wood refinishing help  

Restoration
Dont be tempted to sand it, as far as I can see its in good condition no wobbly joints etc? if that is the case just strip the old finish with a liquid/gel solution (you can get these from a hardware store) as for refinishing you have many options depending on how you like your furniture to look? I dont personally like the gloss finish so prefer a matt or natural finish.

Offer
Oh and I will take up the offer of two for 66 dollars!!

Before using a stripper,
test a small area with acetone. Put some on a white paper towel or rag and rub for 10-20 seconds. If the finish is lacquer, this is enough to dissolve it, then you can proceed with just acetone rather than stripper. Acetone is less messy and I think less expensive.
I had a set of teak chairs that I thought just needed oiling, but turns out they had traces of lacquer finish on them. Because acetone evaporates almost immediately when wiped on, I devised the following method:
1. Wrap the area to be stripped in a cheap white paper towel. (Cheap ones actually hold up better than the pricier super-absorbent ones.)
2. Saturate the paper towel with acetone and let it sit for a bit, patting it with gloved hand to get good contact with the wood. Apply more acetone if needed.
3. After 20-30 seconds, the lacquer should be dissolved and you can wipe it off. No goopy mess that you get with stripper.
4. Go over the wood again with a clean paper towel and more acetone to get any remaining film of lacquer off. Let dry for at least a few hours and then apply teak oil. Use #0000 steel wool if there is any roughness or raised grain, or very fine sandpaper as a last resort.
The paper towel just keeps the acetone from evaporating before it can dissolve the lacquer. This works great with shellac finishes, too (but with denatured alcohol). I devised it when stripping old alligatored shellac off wood trim in a 1910 house that we used to own.

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Spanky words escape me.

Spanky, can you
say why lacquer thinner -- which may be just a bit less likely to flash off immediately -- couldn't be used instead of acetone ?
What would be the test for an oiled as opposed to a hard-film finish -- when the finish is as deteriorated as it appears to be, here ?

Appreciate
all the advice. Its raining here in NYC so I won't will be able to start today as I assume this wouldnt be a safe project to attempt inside my apartment.
So after you use the stripper or acetone, what are the next steps? Was reading a bit online and some say after stripping you sand then stain then apply a finish.

jdip
As I stated above, "Let dry for at least a few hours and then apply teak oil. Use #0000 steel wool if there is any roughness or raised grain, or very fine sandpaper as a last resort."
SDR, I test finishes first with lacquer thinner or acetone, or alcohol if I suspect it's shellac. If neither of these remove the finish, then I assume it's varnish on older pieces or polyurethane on newer ones, or pieces that look like they may have been refinished.
This chair looks like it has lacquer because it's so streaky. It just looks like that---it flakes off completely in some areas but stick in others and keeps its gloss and preserves the color of the wood underneath. But if you oil it, the color won't even out very well.
I can't tell the difference between the evaporation rate of lacquer thinner and acetone. I usually just buy the one that's cheaper!
jdip, wait until you can do this outside on a breezy day, or just invest in a respirator (I got the 3M 7502 on Amazon for about $32 with cartridges---wish I'd done it years ago).

Spanky et al
Thanks. Will give it a try once the weather improves.

I ended
Up purchasing a product by miniwax that contains acetone, methanol and toluene.
Was twice the price of the acetone container but didn't want to make a trip back to home depot if the acetone alone wasn't enough. I attached a pic of the back of the chair taken half way through the job after removing the finish from the right rear leg/backrest support. Overall, the product worked well. So now I have the chair with the old finish removed.
Attached a pic of the side of the chair. The wood on the side looks a fair amount lighter than the wood that is on the back of the shells and the legs.
so now I just oil it? Sorry, I know this is such a novice question but I am learning