It does seem odd.
However, we all know Tolkiens affiliation with the Anglo-Saxon culture and recently my studies have brought me to learning about this culture and its rather difficult language. Be that as it may, the dragon was an important folk symbol that depicted strength and ferocity in battle. Beowulf the greatest AS(Anglo-Saxon) warrior defeated everyone of his enemies until he met his match fighting a great wyrm 'i.e. dragon'.
Dragon and griffon wings were often placed on the sides of helmets presumably to scare opponents with similar superstitions. Later the dragon was taken into heraldric devices and painted onto shields and depicted on banners of war.(e.g. look at the Welsh crest)
One of the popular heroes of the 11th century work of Geoffrey of Monmouth is Uther Pendraag (i.e. of the dragon).
Therefore it is a curious but hardly surprising that Tolkien chose this beast out of his vast bestiary to terrorize the people of Middle Earth. Yet, the use of the dragon helm is not so strange if you look at AS precedents.