Yes, you can play an Event card at any appropriate point. Read the card for further information, such as whether it's considered an "Action" or reaction, interrupt, etc and that will clue you in to the timing involved to play the card.
Jedi Mind Trick
This is an "Action", so you can only play it when you have an Action window, as shown in the flowchart on pages 30-31, in the blue boxes labeled "Player Actions".
Additionally, you will need to spend one Jedi resource, which can be done by focusing an appropriate Jedi-affiliated resource card, which in itself could be an Objective, a Unit, Enhancement, or your Faction Card. Naturally, you cannot focus a card that already has one or more focus tokens on it already.
So using Jedi Mind Trick as an example, you could end your turn, as the Light Side player, with this card in your hand, and lets assume you have a free Jedi resource to spend. On your opponent's turn, they make it to the conflict phase and opt to engage one of your Objectives.
After declaring attackers, and you declare defenders, the Edge battle happens. Let's say you lost the edge battle, and you both have 2 units to attack with on each side. After the edge battle is wholly resolved, but before your opponent would get the opportunity to strike with one of their units, you can then play Jedi Mind Trick in that action window and put a focus token (2 if the Force is with you) on one of the units, stopping it from striking.
At that point, your opponent will still be able to strike first, but only with the unit that was not focused. You will then get to strike with your other two units.
I hope that answers your question.