[Galin]

I checked the Gnomish Lexicon, and there is a Gnomish form (and a Qenya there too):

Gnomish 'bang staff (Q. vanga)'

With respect to Tolkien's sources, generally speaking at least, Carl Hostetter's and Pat Wynne's column Words and Devices (in Vinyar Tengwar) is basically an endeavor to highlight the intended historical connections between the Eldarin languages and those of the Primary World, especially Indo-European.

Of course the question of Tolkien's sources is a complex matter! and (in any case) I am not sure that any of these words meaning 'staff' were retained in the later context of the 50s and 60s versions of Quenya and Sindarin.