Tyrael isn't a great tank, his sustain isn't fantastic, and his crowd control is one of the worst among the Warriors. But what Tyrael does have on every other Warrior is mobility, which he can use to absolutely great effect to harass, chase, pick off, and rescue allies. This build beefs up his sustain through Amplified Healing and Angelic Absorption, while also maximizing damage by combining his auto attack and Smite. Battle Momentum is key to keep his abilities cooled down to keep his mobility up.

Keep Blade of Justice on cool down to chase or flee. Regenerator is a great pick for a purely tanky build, but the damage bonus of Purge Evil adds up quickly, and can help swing team fights. Vampiric Strike is also weaker over the length of a game than Amplified Healing, especially when combining the synergy with Angelic Absorption.

Because of your teleport roots aren't a problem, but stuns, and especially polymorph, can give you headaches. Your best going 1v1 or aggressively pursuing weakened enemies. Try a team composition with another Warrior to take the dedicated tank role, so you're free to play a roaming brawler.