You will notice that the magic weapons described are all swords rather than axes, maces, etc. It is certainly the case that by far the majority of magic weapons are swords, and so we have described all the magic weapons in this fashion. However, players shouldn't feel that they cannot ascribe magic weapons to models carrying axes, maces or other hand weapons. You can either assume the weapon carried by the model has the attributes described for the magic sword, or you can assume the model happens to have the magic sword which he can use instead of another weapon. However, even though a character may have a magic weapon plus another hand weapon he cannot fight with the magic weapon in one hand and an ordinary weapon in the other.
While it is reasonable to assume a magic weapon might be an axe or mace rather than a sword, it is not permitted to assume that a magic weapon is a type of weapon that confers its own combat bonuses such as a halberd, spear, or a lance, for example. Such weapons may be carried in addition to a magic sword/axe/etc.
For example, a hero armed with a lance may charge into combat and fight with his lance instead of his magic sword, but he cannot use the lance's bonus and magic weapon's bonus together, and he cannot fight using both weapons during the same turn even if he has several attacks.