Notes: I've used the Francisca to represent a throwing-style "hand axe"; the German Zweihaender as the big "two-handed sword"; the Arbalest for the "heavy crossbow"; and the padded Gambeson for "leather armor".
This last choice might be controversial, but in a medieval context the most likely cheap armor for infantry (and also, underlying mail/plate) would be the padded/quilted armor of this sort. In this sense, the OD&D listing is in some sense erroneous, but it's possible to interpret it as a leather-fronted "padded jack" (see article link above). If you prefer to go by the text of the 1E DMG ("shaped cuir bouli... cuirass and shoulder pieces", p. 27) then you might consider it Lamellar armor, but that was used mostly in earlier eras or by non-Europeans (e.g., Sumerians, Egyptians, Byzantines). Alternatively, you might consider it the same as a leather Buff coat -- but that's a later European development of the 17th century. Or see here for another take on quilted cloth, leather, and cloaks.
The one other thing that sticks out anomalously for me in OD&D is the Halberd, that being given a significantly more specific identification than anything else on the list. Personally, I let this item stand in for any two-handed poleaxe-type weapon (including a bardiche, lochaber axe, etc.; I'd be happier if it was just identified as a "poleaxe" in the original rules).