Here's my interpretation, fwiw...
Normally when you charge, you must make a melee basic attack. A number of powers can replace this basic attack, such as Howling Strike, Knockdown Assault, Threatening Rush, Ardent Strike, Pounce, Marauder's Rush, Inevitable Wave, Storm Hammer, etc. These are in no means basic attacks. They are simply powers that can be used at the end of a charge.
Other powers such as Eldritch Strike, Grasping Claws, Virtuous Strike, Sonnlinor's Hammer, etc. are actually melee basic attacks, and benefit from everything a basic attack would benefit from (including items such as Bracers of Mighty Striking, and feats such as Impaling Spear).
Having said that, I do wish an item named "Avalanche Hammer" would work for a Barbarian's Howling Strike.