Kakuzu: Overall bad match up. Kakuzu's hearts would get destroyed with one poke, threads are perfect for channeling Chakra to Kakuzu's body if he attempts to grab or strangle Neji, elemental attacks can be shielded and reflected by Rotation or simply avoided, the mask monsters are also hearts, so tey also get one-shotted. Assuming Kakuzu doesn't go all out from the start, like with Kakashi, Neji could easily destroy a good handful of his hearts before he decides to pull them out.
Konan: Rather featless from my memories outside of her prepared fight with Obito. She definitely loses.
Hidan: With intel, there shouldn't be much of an issue with Neji taking out Hidan. Neji can keep himself at a safe distance and would be able to easily avoid Hidan's scythe thanks to his Byakugan and based on his feats against Kidomaru. Wouldn't be impossible for him to intercept the scythe and get rid of it, leaving Hidan completly vulnerable. From there, it would be a simple matter of pumping his body full of Chakra until he explodes. I chakra point being closed would mean no Curse technique, and Neji's speed is on par with Lee's so he's not getting blitzed by Hidan at all.
Deidara: Restricting C0, Neji could easily disarm his bombs by injecting them with chakra in place of using Lightening to difuse them. All of the insight we saw Sasuke display against Deidara would be available to Neji as well, to a much better degree in fact. Only real issue with Neji is that he can't reach Deidara if he flies, so unless he can jump that high, he probably loses simply because he won't be able to touch Deidara. If he can jump high enough to reach Deidara, then he beats him.
Sasori: Chakra strings would easily be destroyed by Gentle Fist, so he can render his opponents useless. He can also use the strings to channel Chakra to Sasori's heart. Puppeteers are also said to be horrible in CQC, and with Neji's speed that rivals weightless Lee's, he can easily close the gap between them and destroy Sasori close up. As for Hiruko, with the amount of force his Rotation displayed in the war, it's possible it could be damaged and destroyed with it. Posion needles and iron sand could also be repelled in this manner.