I'm curious. Could the Glabrezu possibly use a medium creature it's grappling as a "human" shield, potentially gaining half cover, or would a medium creature be too small for that?

Well, those spells are once per day each, as in they can cast each of the spells once per day. It's not that casting one of those three excludes the glabrezu from casting the other two until tomorrow.

Cool, i’ll use him as my warlock’s patron, so the party have to fight him later.

But Not and THEN

Quote from Axefeller >>

Quote from kolovar >>

So here's a fun way to use this guy...

Start with fly - effective for 10 minutes

Next turn, Power word stun an opponent at close range (optional)...if successful, follow through with two pincer attacks...if successful the opponent is grappled.  Use the movement to fly up 60 feet.

Next turn, fly up an additional 60 feet, make 4 meelee attacks, then drop the creature from 120 ft...for an additional 12d6 damage on top of the 4 meelee attacks.  Assuming all are a success, this results in an average of 84 damage.

My players hate this guy.

 

 

I noticed the you said "Next turn, Power word stun an opponent at close range (optional)" Now I must put emphasis on "optional" but still before you "said" "Next turn, Power word stun an opponent at close range (optional)" you "said" "Start with fly - effective for 10 minutes" the Glabrezu can only use one of those.

1/day each: confusion, fly, power word stun

But I must agree with your players, I would hate that guy.

 A little confusion on your end here I think, so for the benefit of anyone still reading this and making the same mistake allow me to clear this up:
It can cast confusion, fly and power word stun once each. So it can do both fly and power word stun as only fly is concentration.

No, they hate you

Quote from kolovar >>

So here's a fun way to use this guy...

Start with fly - effective for 10 minutes

Next turn, Power word stun an opponent at close range (optional)...if successful, follow through with two pincer attacks...if successful the opponent is grappled.  Use the movement to fly up 60 feet.

Next turn, fly up an additional 60 feet, make 4 meelee attacks, then drop the creature from 120 ft...for an additional 12d6 damage on top of the 4 meelee attacks.  Assuming all are a success, this results in an average of 84 damage.

My players hate this guy.

 

Quote from kolovar >>

So here's a fun way to use this guy...

Start with fly - effective for 10 minutes

Next turn, Power word stun an opponent at close range (optional)...if successful, follow through with two pincer attacks...if successful the opponent is grappled.  Use the movement to fly up 60 feet.

Next turn, fly up an additional 60 feet, make 4 meelee attacks, then drop the creature from 120 ft...for an additional 12d6 damage on top of the 4 meelee attacks.  Assuming all are a success, this results in an average of 84 damage.

My players hate this guy.

 

Yeah, that is pretty effective, but goes against their personality. 

"A glabrezu takes great pleasure in destroying mortals through temptation, and these creatures are among the few demons to offer their service to creatures foolish enough to summon them."

So there is a lot more fun to have with them than by just using them as a Bludgeon.  

My friend just sponded this wight in front of a vampire, and one shot it 

"Moving a Grappled Creature. When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you."

A large creature such as the Glabrezu would be slowed unless the grappled creature were small, a huge creature such as a Balor would not be.

Would it be fair pulling this on a party of level 3s 

It doesnt say then. There is no stated order. 

Int 19, hasn't figured out how to use weapons or armor. SMH.

of of of of of of of of of of of

But if they're stunned they shouldn't be able to resist being g dragged