Can Strahd use his Unarmed Strike (that grapples) as an opportunity attack?

Question

New player here and I'm confused about how this works. Any help would be appreciated.

Playing a campaign and we encounter Strahd from Curse of Strahd. The party tries to retreat to sunlight. One member moving away from Strahd provokes an opportunity attack and the DM says he uses an unarmed strike and grapples them. On that player's next turn, they break free from the grapple and attempt to move away. Again, AoO and grappled.

Is this working as intended? Can Strahd use his special Unarmed Strike to grapple as an opportunity attack?

I believe that anything listed under "Actions" can't be used as an opportunity attack. But the DM says AoO allow one melee attack and they believe since Unarmed Strike is a type of melee attack it can be used.

Here is the relevant section of Strahd's statblock:

Unarmed Strike (Vampire Form Only). Melee Weapon Attack: +9 to hit, reach 5 ft., one target. Hit: 8 (1d8 + 4) bludgeoning damage plus 14 (4d6) necrotic damage. If the target is a creature, Strahd can grapple it (escape DC 18) instead of dealing the bludgeoning damage.

Answer 1

Strahd can use the action as an opportunity attack

When you leave a creature's range, you provoke an opportunity attack. The options for what you can do during an opportunity attack are in the Combat section of the Basic Rules:

To make the opportunity attack, you use your reaction to make one melee attack against the provoking creature. 

So your GM is correct. Since Unarmed Strike is one of Strahd's melee attack options, he can use it as an opportunity attack.

Note: the only thing the rules specify is that a monster can't perform the Multiattack option as an opportunity attack ( Monster Manual Introduction)

A creature can’t use Multiattack when making an opportunity attack, which must be a single melee attack.

This is different than the Grapple special melee attack in the Actions in Combat section of the Basic Rules, which specifically requires the Attack action to use.

How do I escape?

Well first of all, the attack can miss meaning it won't grapple since it won't deal bludgeoning damage to replace with the grapple. As such, any way for your allies to increase your Armor Class (i.e. shield of faith) or decrease Strahd's attack roll (i.e. vicious mockery) will make it easier to escape.

Grappling restricts your movement but it doesn't mean you can't change your position in other ways. Teleportation is the easiest way, such as with misty step. Also, freedom of movement let's you break free of a grapple by spending 5 feet of movement.

Also, if your allies move Strahd away from you (with an effect like the Shove special melee attack from a Rogue who can take the Cunning Action to disengage) then the grapple will be cancelled and you can move away.

Lastly, you could prevent Strahd from using a reaction (which is required for an opportunity attack). The easiest way to do this is using the shocking grasp spell (perhaps delivered by a wizard's familiar), but you could also force him to use his reaction on something else.