You can recruit the Red Immortals after you take them as prisoners.
Camp -> Take an Action -> Recruit some of your prisoners to your party.
You'll probably have to knock them out yourself to do it though. If you send in your own blunt weapon cavalry to take them out, they'll likely get shredded by the Immortals.
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HP and Armour: Immortals have 115 hp, 58 head armour, 75 body armour, 53 leg armour. They're VERY tanky, and while their armour isn't the best in the game, it's not awful either.
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Weapons: They use an Ancestral Greatsword (2h/1h weapon, 54 cut, 48 pierce, 108 speed, 111 range), Pila (Throwing weapon, 60 pierce, 85 speed, Bonus against Shields) and the Old Age Steel Shield (400 hp, 40 resistance, 90 size, speed 85). Their weapons are very good, and they're amazing at using them.
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Ranged Strength: Monstrously deadly. Their Pila, with 600 Throwing proficiency and 10 Power Throw with the 60p + Bonus to Shields are pinpoint accurate and take out the best shields in the game (other than the Aegis) in 2 or 3 hits. If they hit you, you're dead in two hits at most. Fortunately, they only have 4 shots each.
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Melee Strength: Godlike, probably the best unit in the game that's not a Hero. They're
300's Spartans with bastard swords. 115 hp, Str 60, Agi 43, Power Strike 10, Athletics 10 - they hit extremely hard and they're insanely fast despite their heavy armour. They will quickly mob any blunt weapon cavalry you send in and cut them to ribbons with the Ancestral Greatsword. If you send in your whole army, you'll take heavy losses and forever lose the chance to use these wonderful infantry yourself.
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So what do you do, if your own blunt weapon cavalry will die in their droves?
You take a strong, fast mount (Perisno Twilight Horse or Wyvern), 3 very strong shields and a Jousting Lance. You're going to ride around them in a circle until they use up all their throwing weapons, and then send in your companions with blunt weapons. Your companions should manage to take out a couple of them, and during the distraction you should be able to take out 5-10 Immortals.
After that, you'll ride around the enemy mob with a couched lance being very careful to not get hit. If they hit the nose of your mount before you hit them with the lance you can very quickly find yourself dismounted.
It doesn't matter too much if you get knocked out early, as long as you've knocked out about 20-30 of them that round. Keep doing it and you should soon have the entire party of Red Immortals as prisoners.
Take care of them. They're incredible in sieges, though they don't use their shields as often as I'd like, so keep them hidden amongst your other infantry. I keep 10 of them at the bottom of my party, and I break them out whenever I need to break a meatgrinder in a particularly bad siege.