Which level are you? There are a couple things you might try.
Spamming summons is one of them - plague of undead is kinda powerful, the dead walk might provide unlimited meat.
As for SR, it is a pain in the ass especially if you lost warlock levels. Abandoning hellfire warlock, however, won't help with that - hellfire warlock advances invoker level as it should. delaying hellfire warlock until higher levels would only gain you 1 BAB. Abandoning shifter would also gain 1 BAB, but lose you the dex you get from the shape.
You could also try getting scrolls of mantle of egregious might, greater heroism, create magic tattoo for +12 AB in total. Other spells that come to mind are divine power, righteous might, battletide, prayer, blessing, divine favor...
Hellfire shield delivers eldritch blast damage and requires a reflex save, so it would hit, no idea about the SR though.
As far as Wall of Perilous Flame goes, it is bugged in that it deals (2d6+1)*Invoker Level damage instead of 2d6 +1*Invoker level. It still shouldn't penetrate SR automatically, but since you can stack that there's a high chance it will hit eventually. Then you can just Flee the Scene to the other side of the flames.
Lost Boy - eldritch chain on a lackey won't work as every creature struck requires a separate touch attack.
Overall practiced invoker is your friend, Since you need to be level 9 to get hellfire warlock and you were hfw 3, I guess you were level 12. With practiced invoker you would get one greater invocation leaving you with 3 least, 1 lesser, 1 greater. If you chose to pick warlock at level 9 you could get another least invocation through extra invocation. You could also get weapon focus ray for another +1 to attack - no idea if that would help though as I don't know the AC of the blue dragon - is it an adult blue dragon? If yes, his AC should be 28 - no idea about the touch AC though.
What to do with those: I like the trick with darkness+devil's sight, but I think dragons true seeing nullifies that. Summon swarm? Probably will not punch through DR. Beguiling influence helps avoid fights, while dark one's own luck helps with what Lost Boy said. Lesser invocations have chain, baneblast adds damage, but doesnt help punch through SR or hit, so pass. And you can't hit him with eldritch chain anyway... I dont think anything here helps you that much except flee the scene for running and ignore the pyre for elemental damage resistance. Oh, and the dead walk to make a meat shield.
Greater invocations is where its at: wall of perilous flame won't punch through SR but thanks to a bug deals immense damage. Stackable. Eldritch cone and line let you target reflex save with your EB, but won't punch through SR. Vitriolic blast is amazing, but you have to hit the touch attack. I believe the best option is to get chilling tentacles and stack the hell out of them. They ignore SR, deal bludgeon damage, on failed save root the dragon in place (won't happen often - but you STACK the tentacles) and deal 2d6 cold each round - I don't think there's a save on this. Just spam it and run in circles. Flee the scene and ignore the pyre should work just fine for that.
TL;DR
Get chilling tentacles, with practiced invoker you can get one greater invocation at level 12 and it should be this one.
Also send me a save and your char and let me try.