Federation Commander

Is the overload action only of use if you fire in the turn you overload, or is it setting the overload flag to true, so that your photons are now overloaded and can be fired as such in any subsequent turn as overloads without using the action?

It reads like the latter, but I'm bit unsure of special actions, some seem to be setting a flag to true so to speak (cloak = true, loaded = true) others seem to only apply during the turn that they are used (EM, boost shields).

It can only be used during the turn it is selected.
But if you select Overload Weapons and there is a better target outside of overload range, you can still fire at the the longer range... you just do not gain the benefits of the overloaded weapons.