Describe the following to your players to provide better immersion - (show, don't tell during their first encounter): 

A tiny fiend with leathery batwings, a barbed tail, and sharp, twisted horns flutters at about eye level, winking into sight from out of thin air.

In addition, you might want to allow them an Intelligence - Religion check to know the following (accumulated - a roll of 25 or above would know all):

DC5 (very easy): attacks with its stinger

DC10 (easy): is invisible until it attacks - ability to fly

DC15 (medium): resistance to magical spells and effects - damage resistance to cold, bludgeoning, piercing, and slashing from nonmagical attacks that aren't silvered - does not have damage vulnerabilities

DC20 (hard): attacking the creature with fire or poison has no effect

DC25 (very hard): immune to being poisoned - darkvision out to 120' and can see within magical darkness - ability to polymorph into a rat, a raven, or a spider

With this or the Quasit as Pact of the Chain familiars, you can just keep them in their beast forms all the time if you want.

They'll still be able to talk, turn invisible, inflict poison, etc.

The imp actually flies faster when it's a raven!

This was really helpful as a new GM thanks

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10/10 familiar, playing as a tiefling warlock with a dark past with her fiend

Quote from Gay_Dog >>

With this or the Quasit as Pact of the Chain familiars, you can just keep them in their beast forms all the time if you want.

They'll still be able to talk, turn invisible, inflict poison, etc.

The imp actually flies faster when it's a raven!

 true....but they lose the valuable ability to use their hands for fine tasks, and  wear any equipment such as: shield, many handed pouch,  or mythrial chainmail. if you wish them to be covert....they can just be invisible. An (with their equipment as well) . A creature with truesight would see the creature is polymorphed as well.Any creature with detect magic would see the school on the creature. However detect magic will not reveal invisible creatures. 

As a DM I *love* using imps in my fights. I have them turn invisible and attempt to sneak attack casters in the back while tanks focus on bigger targets in the front. They don’t do a lot of damage with their sting but really force squishy targets to stay on their toes. I usually have them “flee” and pop up again in later fights to break up formations and get people to split forces 

When an imp or its raven form flees, it provokes an attack of opportunity.  I wish its raven form had flyby like an Owl familiar.  Flyby is good for delivering touch spells (like touch spell attacks or healing for celestial warlocks),  help actions, etc.  Allows mobility on the battlefield.  

Not if the DM gives them invisibility as a bonus action 😉

True.  Just not rules as written.  Rules as written indicate it takes an action 

Yeah. I find many stat blocks need a boost to prevent parties one shot bosses in the first round 

An invisible imp can use the help action without breaking invisibility. It can tug on the target’s hair, scream in its ear, tickle it under its chin, etc - as long as it’s not making an attack, it can remain invisible.

I believe you’re right!  Yay!  Been reading several forums.  Now I might change from stone to Chain. 

How can I print this so I do not need to have a computer at my Gamming table?

Quote from Edrick1976 >>

How can I print this so I do not need to have a computer at my Gamming table?

 Unfortunately, you’re going to have to copy/past, or take a screenshot.

Also as a Celestial warlock it can deliver a friendly touch spell like a heal without breaking invisibility, because it is not an attack.

Wrong edition.  In 5th, ANY spellcasting breaks invisibility.  

Invisibility

A creature you touch becomes invisible until the spell ends. Anything the target is wearing or carrying is invisible as long as it is on the target's person. The spell ends for a target that attacks or casts a spell.

You want the improved version.

Greater invisibility

You or a creature you touch becomes invisible until the spell ends. Anything the target is wearing or carrying is invisible as long as it is on the target's person.

No, it was correct they way I had it.

The imp is not casting a spell, the warlock is, the imp is just delivering it and it is not an attack or a save.

If they tried to deliver shocking grasp it would break invisibility, due to being an attack, healing will not

Do you have any source that indicates that delivering a spell is any different the casting it?  It's still being the conduit for a spell which breaks invisibility. The fact that it's healing, not an attack is irrelevant.  It explicitly says attacks or casts a spell. Now, he could administer a potion or a goodberry to get someone back on their feet without breaking invisibility.  

Simple, the imp did not cast a spell, the imp just delivered the spell, same as he would deliver an item, open a door, or use a potion.

The warlock spent the spell slot, provided the components of the spell and cast it, it just was channeled through the imp.