A brake noodle is the bent tube used to redirect the cable into a V-brake. (looks like a pice of elbow macaroni)

To the OP

Yes, the cable should run smoothly within it since you don't want a new source of friction. However if there's a kink in the wire it's bind. Sometimes, the liner is a bit closed inside, or shifted down to the point which pinches it. Thread the wire to a good, non kinked area and wok it back and forth.

Noodles are pretty standard and will accommodate any brake cable up to shy of 2mm or so. This is standard so there's no reason for anyone to make a noodle that won't handle that.

However, in the past some cables were larger than 2mm so if you're using an old cable it may be oversize.

Measure, check and confirm that all is good, and go from there.