Let's pretend that I am at the start of the combat round. My opponent and I each have a hero locked in combat one with another. We each call a heroic action. I call a heroic combat, and he calls a heroic strike. We resolve the toss to see who is allowed to resolve their action first and I win the toss. Therefore we resolve the combat. Does my opponent still get to roll to increase his Fight as he called a heroic strike? Or does he lose the opportunity as my action will be resolved first?

Combat go's 1st no roll off required.
His hero gets to strike in the combat.

When both players call heroic actions a roll off is always required to determine who can perform their heroic action first. See page 57. Thus, if I'm permitted to resolve my action first (the combat) I understand the rules to mean that my opponent who called a heroic strike would not get to increase his fight as his action would not be activated until After I resolve my combat action, correct? Or would the heroic strike occur inside the other heroes heroic action?

There is no need for a roll off because of the different nature of the action.
Heroic combat makes the hero fight first and strikes are resolved before duel rolls. There's no competition between those actions.
Like movement and channeling.

Dikey and Steven are right on this. Pg. 57 says that role offs are only needed when two of the same actions are called when those actions are ones that disrupt the regular order of operation but not just any two actions. Heroic Strike is resolved when the hero who called it has their combat resolved which could not be interrupted by a heroic combat.

_________________
"Draw your sword with a heavy heart, but swing it with a heavy hand"

Then in this scenario, my opponent would get the fight value boost at the start of the heroic combat which I called?

That is correct.

_________________
"Draw your sword with a heavy heart, but swing it with a heavy hand"

Great thanks!