Just untwist as much as you need to connect to your LEDs. Then leave the rest twisted until you get to the power input.
This wire is 30awg, which is very fine. The wire does not have a bulky rubber jacket. Instead, it is coated with enamel and then polymer for a tough durable coating. Strip with sand paper or with your solder iron.
How to strip this wire?
Magnet wire has a tough outer jacket and it just can't be stripped with wire strippers.
We thought this video would help:
Strip the wire with sand paper, flip the wire over to get the other side stripped. When you are done, the wire should be shiny copper, all ready for connecting. Don't sand too far, you don't want to damage the copper underneath.