Who has the priority to use their abilities first in the following example:

X-wing with a target lock on Soontir with an elusive upgrade. I roll blank, blank, hit, crit and want to use my target lock. But Soontir wants to also make me reroll my crit with elusive.

Consequences: I use my lock first and reroll my blanks into hit and hit, then reroll my crit result. Or, Soontir makes me reroll my crit, I roll out a blank. Now I can use my target lock but am stuck with the blank from the elusive reroll since you can't reroll a reroll.

Also, first post and just got into the game 2 weeks ago. So much fun!

Defender modifies attackers dice first. Attacker modifies defenders dice first.

According to the rules (page 11) the defender gets to modify the attacker's roll first, then the attacker gets to modify the attack roll. So in your example, your opponent gets to use their ability first to modify your attack roll.

The situation is reversed for defense rolls, in case that comes up (page 12). In short, the person not rolling the dice gets to modify the roll first.

Edit: Ninja'd... Well at least I put in the page numbers too...

P.S. You can only re-roll a particular die once . Other things may modify it but you cannot re-roll a die that you have re-rolled.

Reroll: Some effects allow players to reroll certain dice. To resolve this, the player picks up the appropriate number of dice from the common area and rolls those dice again.

Important: When a die is changed or rerolled, ignore its original result and apply only the new result. This
new result may be modified by other effects; however, a die that has already been rerolled cannot be rerolled again during this attack.

To rephrase what KaS is saying: If Soontir forces you to reroll your [crit] you couldn't re-roll it with your TL anyway and for some reason I doubt you would have wanted to re-roll it with the TL. Even if the process is messed up it seems you're getting the right final result goat.