Question about Pummeling / Jabbing Style Feats

[JuliusCromwell]

can they be used with weapons such as The Axe Knuckle , brass knuckle and other such punching weapons or is it just plain Unarmed strikes?

[Fuzzy-Wuzzy]

Jabbing and Pummeling Styles work with any kind of unarmed strike, so if the weapon specifies that using it is still an unarmed strike (like brass knuckles or a cestus does; not positive about axe knuckles) you're set. You still need the Improved Unarmed Strike prerequisite feat, though.