For reference I'm playing a monk X / war cleric 1 / maybe fighter 2 but this could be for just a straight up fighter as well.

- Thrown weapon style allows you to draw a weapon with the thrown property as part of the attack made with the weapon.

- The Javelin of Lightnings ability is part of the attack made with the javelin (there's a Crawford tweet somewhere that confirms this)

- The efficient/elhonna quiver can store a butt load of stuff including javelins 

Does this mean, given the ability to make multiple attacks in a turn my character could throw three (2 attacks + War Priest), or a straight up fighter could throw as many as 5 (without action surge)?

As a monk/war cleric you would get 2 thrown javelins (starting at L5) + 1-5 bonus javelins from the war priest feature. You would not get more than 5 such bonus attacks per day (1 long rest per day). As a fighter/ cleric it would be 3 attacks + the 1-5 bonus javelins per day not 5 as you never get the 4th attack (at L20) since you took at least 1 level in cleric. Javelins of lightning are useful as the bolt changes a 1D6 30’ range weapon into a 4D6 130’ AoE + a 120’ 5 d6 attack usable 1/ day/ javelin. Javelins are not one of my preferred weapons as the range is only slightly better than a handaxe or dagger. Javelins of lightning are a far better weapon but because of that you are unlikely to get enough of them to fill Ehlonna’s Quiver (18). In older editions they were single use items not daily use so they sometimes were found in multiples, that shouldn’t be happening in 5e. That said, I can potentially see a high level character acquiring up to 5 giving them enough (potentially) to cover their war cleric bonus attacks.

For the Monk, if you use the Ki-fuelled Attack optional class feature from Tasha's Cauldron of Everything then you can use that to supplement War Priest by also gaining the bonus action attack whenever you spend a Ki point as part of an attack during your action.

There aren't a tonne of ways to trigger this, easiest is on Way of Kensei using Deft Strike (adds bonus damage) but there's also the other optional class feature Focused Aim which lets you add Ki point(s) to potentially turn a miss into a hit, and would count for triggering the bonus action attack; since a javelin of lightning still makes an attack roll then this qualifies.

This can save you some uses of War Priest, by instead using abilities that refresh on a short rest, so it's a handy thing to have available.

One interesting thing to note with the monk - Kensai is that javelins are listed as a melee weapon not a missile weapon in DDB. I don’t know if this is a bug or a feature? But it is annoying as that means you can’t take it as the Kensai missile weapon. The concept of a monk armed with a bunch of javelins of lightning is interesting but fairly unrealistic I think.

The javelin is a melee weapon even when thrown, not a ranged weapon.

Quote from Wi1dBi11 >>

One interesting thing to note with the monk - Kensai is that javelins are listed as a melee weapon not a missile weapon in DDB. I don’t know if this is a bug or a feature? But it is annoying as that means you can’t take it as the Kensai missile weapon. The concept of a monk armed with a bunch of javelins of lightning is interesting but fairly unrealistic I think.

As Plaguescarred says a javelin is a melee weapon so you can take it as a Kensei melee weapon as well; but when you throw it (which you need to to make full use of a javelin of lightning) you're making a ranged weapon attack with it, which is why Deft Strike works for Ki-fuelled Attack but Stunning Strike doesn't (the latter works for melee weapon attacks only).

Thanks to all above this has and hopefully continues to be a great thread for me to learn from.