"Whenever you use your eldritch blast ability, you can change your eldritch blast into a hellfire blast."
Note that it doesn't say "cast." "Using" your eldritch blast ability can either be thought of as making an attack with it, or in the case of claws or glaive, the initial forming and then using. So there seem to be four possibilities:
1: Claws and/or glaive don't allow for Hellfire Blast (referred to as HB from now on) because it's not "casting" EB. Which is kinda silly really. Or perhaps someone doesn't like the wording of it and thinks it'd be "OP" to have the extra damage apply on each hit.
2: Claws and glaive would only get the bonus for the first hit. This is possibly the most balanced option if someone thinks the damage only ought to be once per round since that can be seen as Read As Intended.
3: Claws and glaive trigger the Con damage on each hit. Though possibly in line with the intent of the class features, it's a massive douchebag move because of the number of attacks possible with each.
4: Pay 1 Con point to grant HB to all EB attacks for the round (including any AoOs made). This is what most people who know that damage isn't everything (or in the cause of power gamers, think damage is everything) would advocate for.
It'll be up to the DM though. Some games could handle 4, but others would be best with 2 or 1. 3, as mentioned, is just a giant douchebag move given the fact that it's Con damage that would apply for each attempted hit.