Yes, players get priority between first strike and regular damage steps; so they can cast spells, and state-based actions will be checked, and triggered abilities will resolve.
First strike and double strike create an additional combat damage step; pretty much just like the normal one. And players get priority after damage is done during the combat damage step. So in your example, you would be able to prevent any regular combat damage from being done by destroying creatures after first strike damage was done.
- Combat Damage Step
510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.
510.4. If at least one attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step.