Oath of Vengeance maximizes your combat damage
We’ll focus on damage output as that seems to be what you are concerned about based on the points you consider. Spells like sanctuary also have useful defensive applications in combat, and spells like zone if truth outside of combat, but from how the question is written, you ignore all these aspects for determining what is “better”.
Much of this will depend on what opponents you will be facing. Without information on the campaign world, we'll assume a "generic" setting populated with MM monsters whose CR is matching character level. We'll also ignore foes dying before the end of combat to simpify.
Base Numbers
The average 5e fight in theory takes about 3-4 rounds, and in practice often takes 4-5 rounds. We will assume four rounds. You thus can expect to have 4 actions and 4 bonus actions. Each is worth one attack. A lot of this answer will come down to action and bonus action economy, and thus is stongly influcened by the number of rounds you expect to fight.
Average raw damage: each of your attacks is Greatsword 2d6 for 7 points, +5 from stat, for a total of 12; more if you have a magic weapon, Great Weapon Fighting, are a Half-Orc etc. You can hexblade curse as a bonus action first round, for +5 damage plus double chance for critical wich adds a fractional point of damage we'll ignore. As it resets each short rest, let's assume use can use it every fight. This will boost your damage to 17. If you activate Great Weapon Master (GWM), add 10 for 27 total.
Average chance to hit a level-adequate monster based on expected AC without advantage or disadvantage is about 65% without magic weapons. GWM reduces this to 40%.
Net damage from attacks is average chance to hit times average raw damage. Either way, you are looking at 11 damage per attack. In practice, you will likely do quite a bit more, as you can select normal attacks for high-AC, and GWM attacks for low-AC foes.
Advantage helps to offset GWM's downside. The numerical effect on GWM's 40% to hit is 24%, worth about 6.5 net damage (5 without curse). We'll use GWM when you have advantage.
Advantage doubles your chance for criticals for extra divine smite damage. As a hexblade 8 / paladin 3 you'll have a lot of slots to burn. Even with hexblade curse you are unlikely to get more than 1 crits, so you can burn high level slots for raw extra damage of 22.5, or added average damage of 2 points per attack (1 without curse). This brings damage to 8.5 (6 without curse).
Devotion
Adds protection from evil and good, sanctuary, lesser restoration, zone of truth.
None of the spells has direct damage impact. Damage contribution: 0.
You can sacrifice one action worth 11 net damage for Sacred Weapon to add a full +5 to attacks, worth 7 damage each with GWM, which will net you a damage contribution of 3*7-11 = 10.
Actions will be worth two attacks after you get Extra Attack at Paladin level 5; then Sacred Weapon will cost you two attacks, and add the bonus to 6 attacks, for a contibution of 6*7-22 = 20.
Total damage contribution: 10 (20).
Vengeance
Adds bane, hold person, hunter's mark, misty step.
Hold person at base value is about damage neutral. I omit the detail calculations, the post is long enough as it is; if you use divine smite or others also attack the victim it is accretive. At mid to high CR humanoids are uncommon, so it will not apply most of the time. Bane and misty step have no direct damage impact. Hunter's mark adds 1-2 damage net per attack, but you you already have it, so the Oath does nothing. Net damage contribution from spells: 0
Vow of Enmitiy gives advantage, adding 6 net damage to attacks without hexblade curse. Since this is more than hexblade curse's contribution of 2 damage, use it first turn, for +4 improvement that turn. Then use curse with your second bonus action to get 3 attacks with +8.5 net each. Hunter's Mark comes one round later, -1.5 damage. Damage contribution: 4+3*8.5-1.5 = 28.
Actions will be worth two attacks after you get Extra Attack at Paladin level 5, then the vow will yield twice that, or 56 damage.
Total damage contribution: 28 (56).
Conquest
Adds command, armor of agathys, spiritual weapon, hold person.
Command nets you no damage, a prone opponent adds 6.5 from advantage per attack for 11 you give up with your action. We discussed hold person already.
Spiritual weapon adds a bonus action meelee attack of d8+5 force damage per round, at 65% hit chance worth 6 net damage. Hexblade curse adds more over the fight than one such attack, so use that with the first turn bonus action and spiritual weapon with the next three. You won't be able to cast hunter's mark, losing about 4 damage. Damage contribution 3*6-4 = 14.
Armor of agathys costs you an action worth 11 net damage (later on 22) to recoup 5 points whenever you get hit. This will depend how often you get hit. If you expect more than 2 (later 4) times, it will be worth it. Damage contribution: ?
You will gain +10 to one attack with Guided Strike, or 50% increased chance to hit, worth about 14 points of damage with GWM. Damage contribution: 14.
Total damage contribution 28.
Conclusion
By this reconning, Oath of Vengeance or Oath of Conquest are best with Oath of Devotion far behind. In the long run, Oath of Vengeance will be stronger.
