I'm a bit torn on the Neesham selection. Despite generating good pace, I think he needs to either do a bit more with the ball or reduce his frequency of completely wild deliveries to be selected in a primarily bowling role for Test cricket, and while his batting has enormous promise he hasn't quite developed it to a the standard required to be a frontline batsman in First Class cricket either. One day cricket is a different story, but I think even he'd admit he isn't quite where he'd like to be just yet in the whites, despite the good numbers this season. I think, if he were to play Test cricket, his best role currently would be batting 7 as the fourth seamer with a specialist spinner in the side and a wicket keeper capable of batting six above him. In a world where Vettori hadn't unofficially retired and Anderson never recovered from injury, Neesham would be a great pick. As it is, I don't think he'll have much of a role.
That said, I'm not quite sure what I'd do with Sodhi's position. Kane Williamson is the best spinner in New Zealand barring the possible exceptions of Vettori (pseudo-retired) and Patel (tried and failed), and Anderson's ability to perform as the fourth seamer would be wasted completely by picking four genuine bowlers. New Zealand have effectively been playing with ten ever since Sodhi debuted, so maybe the best option is someone with a lot of talent who could theoretically contribute heavily with either bat or ball but isn't necessarily expected to. If he fails with the bat then it doesn't matter too much because he's at eight and if he doesn't bowl well then Anderson and Williamson are there too.
I can't shake the feeling it's a bit of a nothing role and that he'll contribute very little as it is, but at the same time I can't really offer an alternative that isn't a waste of resources.