Phrase referring to several Viking polearms
The term "halberd" has been used to translate several Old Norse words relating to polearms in the context of Viking Age arms and armour, and in scientific literature about the Viking Age. In referring to the Viking Age weapon, the term "halberd" is not to be taken as referring to the classical Swiss halberd of the 15th century, but rather in its literal sense of "axe-on-a-pole", describing a weapon of the more general glaive type.
Instances in literature.
In English translations of sagas, "halberd," "bill," or other terms have been used to translate several different Old Norse words. It is thus difficult to know what kind of weapon is being described in these translations, or the original texts. Many of these terms are shown below.
Atgeir.
The "atgeir" was a type of bill or halberd, from Old Norse "geirr", "spear". The "atgeirr" is thought to have been a foreign weapon and is rarely mentioned in the sagas, but is famous as the favorite weapon of Gunnar of Hlíðarendi. In Njál's saga this weapon is shown as used mostly for thrusting, but also for hewing.
Höggspjót.
The "höggspjót", literally "hewing spear", takes its name from Old Norse "högg", "stroke, blow, slaughter, beheading" and "spjót", "spear".
Kesja.
The "kesja" was another halberd-type weapon. The name is thought to come from Celtic-Latin "gæsum". The Cleasby and Vigfússon dictionary notes that ""kesja", "atgeir" and "höggspjót" appear to be the same thing". It's interesting to note that "Egils saga" shows the "kesja" being thrown like a javelin or spear, and describes it in detail, calling it also a "mail-piercer" ("brynþvarar"):
The "kesja" would thus have a blade around 90 cm in length with a diamond cross-section at the end, and an additional spike attached to the socket, whose placement and purpose is not explained. The length of the weapons' shaft is unclear, but was either shoulder-height, or long enough that a man reaching up could still touch the socket.
Krókspjót.
The "krókspjót" was a barbed spear, literally "hooked spear", from Old Norse "krókr", "hook, anything crooked", and "spjót", "spear" (cf. "höggspjót", above). The "krókspjót" resembled a regular spear, except that it had two lugs or "wings" attached at the bottom of the spearhead, somewhat like a boar-spear. Additional hook-spear types have been found from the period, used for hunting fish, seal and whale. 
Skeggøx.
The "skeggøx", literally "bearded axe", was called so because while the blade was narrow at the haft, it widened downwards towards its edge, so that the "face" of the axe seemed to have a drooping "beard". The name is from Old Norse "skegg", "beard" and "øx", "axe".
Archeological evidence.
The term "Viking halberd" was used to describe a find in North America in the 1995 book "Early Vikings of the New World", but it was later demonstrated to be a tobacco cutter.
There has currently been, in fact, no clearly identified Viking halberd or bill found. Spears are the only type of polearms found in Viking graves. It is possible that halberds and bills were not part of Viking funerary customs, as opposed to other weapons that have been found in graves. Bills have been found in Frankish graves from the Merovingian period, which predates the Viking Age; but their use by the Scandinavians is not attested and, if existent, seemed to have been rare.
References.
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