My reading of all three abilities comes to the conclusion that while your aasimar transformation is active, one eldritch blast attack would have extra damage equal to your level + your Charisma mod, and the rest would just have your Charisma mod (from Agonizing Blast).
The Protector Aasimar's Radiant Soul trait (VGtM, p. 105) says:
[...] once on each of your turns, you can deal extra radiant damage to one target when you deal damage to it with an attack or a spell. The extra radiant damage equals your level.
The relevant portion of the Scourge Aasimar's Radiant Consumption trait is worded identically.
Secondly, the Celestial warlock's 6th-level feature, coincidentally also named Radiant Soul (XGtE, p. 55), reads:
[...] when you cast a spell that deals radiant or fire damage, you can add your Charisma modifier to one radiant or fire damage roll of that spell against one of its targets.
Eldritch blast does not do radiant damage, it does force damage, so the extra radiant damage from the Aasimar's racial trait would not trigger this feature.
The extra damage from Agonizing Blast would work fine though.