If I have one of the Skald's at-will powers such as Bolstering Speech that triggers when I hit with a basic attack through Master of Stories and the half-elf 1/encounter at-will, can I trigger its effect off of a power that says it can be used as a basic attack?
It depends on the exact writing of the power.
The Warlock's Eldritch Strike has "This power counts as a basic attack." So all things that trigger on basic attacks do so.
However, powers such as the Paladin's Ardent Strike have "This power may be used in place of a basic attack while charging" and do not count as a basic attack, because it is only "in place of".