There is no archaeological evidence for a Viking weapon that could be described as a "halberd" or "bill". There are spears and there are axes, and ne'er the twain shall meet (or at any rate they haven't yet).

Skaldic (poetic) language was often employed in writing Old Norse, and typically accounts for the existence of words that might seem to identify specific types of weapons, but in fact are "flowery" words that alleviate a writer's sense of monologophobia.

Add to this some over-eager later lexicographers trying to interpret these words based on their context, and a limited knowledge of archaeological evidence and you have "Viking halberds"

A perusal of the lexicon of Old Norse (and indeed /r/Norse might have been a better place to ask this) reveals the following terms for "halberd":

• atgeirr: descendants of this word are generally agreed to mean "spear", with at- basically synonymous with the English word, and geirr meaning "spear".

• bryntrǫll: this word means "mail-troll", bryn- "mail", and trǫll we borrowed from ON. I'd interpret this as a weapon that damages or pierces armor; a spear, another name for brynþvari.

• brynþvari: "mail-piercer" (þvari = related to þvarg, "quarrel" = pierce); spear.

• hǫggspjót: "blow-spear" (hǫgg = "blow", spjót = "spear"); spear.

• kesja: this appears to be the name of a specific kind of spear.

• skeggja: a poetic term for "spear", or possibly "axe", related to skegg, "beard".

It has been argued (Hjalmar Falk, Altnordische Waffenkunde, 1914) that the terms brynþvari, and kesja describe a pair of specialized spears, the former having a narrow, spike-like point, and the latter, a broad blade. There are examples that match these descriptions, but linking these words with these artifacts has proven problematic (see K. James McMullen, "War Words and Battle Spears: The kesja and kesjulag in Old Norse Literature", Journal of Medieval History, vol. 12).