All the damage Skirk Fire Marshal would deal to creatures and players will be prevented. The damage is dealt in a single event, so the "next time" part of Awe Strike applies to all of it.
Awe Strike doesn't specifically say it only works on combat damage, so that means it can prevent any kind of damage a creature would deal.
December 8, 2018 10:13 a.m.
Milesprower87 - in the future, please be sure to hit the "Mark as Answer" button appearing next to each responsive post when your question is resolved. This helps keep the Rules Q&A section clutter-free and helps future users quickly identify the correct answer.
As you have indicated you have had your question answered and no longer need assistance, I have gone ahead and marked an answer as accepted. If you could try to remember to do this in the future, that would be appreciated.