need help with 3.5mm audio plug wiring

I bought a bluetooth adapter which I was planning to hardwire into my car and into my stock stereo by feeding the audio into my XM reciever, being I don't subscribe or use XM. Being I wanted it hardwired, I cut the wire just before the plug expected to see 3 normal wires - one being ground, one being left + and one being right +. By normal, I mean a wire with insulation which when stripped would either be braided or non-braided wire inside the insulation.

On this particular wire though, it is very odd. It was very thin, and when I stripped the main/black insulation there were 3 colored wired, but not the usual rubber insulation with a wire inside. Instead the outer color is strained wires and if you unwind it, inside is just a nylon string which I believe gives the wire its pull strengh. Thus it is almost like the outer strands are the wire, but that woudn't make sense since all 3 would touch each other. Further I got out my multimeter and I have no continuity between either the outer strand or inner nylon when touching the plug ports. Not sure if I described it well, but hopefully someone may know what type of wire I have and how to properly wire this.

Thanks
 
OK - here are some pics - you can see there are 3 colors but the outer material is not the usual plastic/rubber but rather some type of stranded metal wire - if you unwind it you will see that nylon string. I put my multimeter on both the metal strands and to the nylon and neither has continuity to the plug. I have another 3.5mm plug with usual type wires and when I strip the 3 colored wires I get continuity when touching the plug. So this is why I'm so confused, as I can't find the actual wire that connects to the plug ends???

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You still seem uncertain, so I've zoomed into your photos.

I see two signal wires either side of a screen as would be used to wire a 3.5mm, 3 pole jack plug.

Please let us know if you found Leadbelly's advice to be useful.
 
If you don't believe me, you can carefully scrape off some of the enamel with a very sharp blade. You will find copper underneath; you can test that for continuity to prove it to yourself.

I would however snip that off before you solder. You want every single bit of the thin wire inside your solder connection.
 
This is intended for headphones or headsets, so un-shielded.
As long as You don't use a long cable, You should be fine with hum pickup.
The white nylon is for strain relief. Some cables use the yellow Kevlar instead.
A lighter or an x-acto knife can help exposing the copper from the enamel.