I was confused about that too. Sounds like he's asking about wires running from the battery to the atomizer.
You could probably get away with 26 AWG if your wires are short enough, but I wouldn't go that fine unless I really had to. I tend to use 22 or 20 gauge whenever possible. 18 gauge is not out of the question.
You can look up wire resistance easily enough and determine how much power you're going to lose in the wiring. For example, 26 AWG has about 40mΩ per foot. If you use 6 inches to get to the battery and back, that would be a power loss of 80mW at 2A. Compared to the 7.4W of the load that would be a loss a little over 1% in the wiring. Probably acceptable, but you could quarter that by using 20 AWG wire. Also, resistance goes up considerably with heat and the smaller wire is going to heat up faster. Power loss goes up considerably with heat as well.
I like solid wire a lot since I find it easier to work with. I'm not sure if the electrical properties are better or worse, but you can figure a cross section of solid wire contains more copper area than a cross section of stranded wire.