There are two Warlock twins, Boris and Doris, who have made a deal with a celestial entity to cleanse the evil from the world. In one of the catacombs they are exploring they encounter a skeleton. Boris, with the higher initiative roll, reacts to the skeleton first and moves to the skeleton's left while preparing to fire an eldritch blast (using the Ready action) using the Repelling Blast invocation at the moment that his sister uses eldritch blast; this is intended as a way to apply a combo attack.

Doris remembers that skeletons are particularly weak to being crushed, so she gets an idea moving to the right side of the skeleton and firing an eldritch blast, also with repelling blast invocation, thinking that when she and her brother fire at the same time the skeleton will be crushed due to the opposed push by two Repelling Blast-empowered eldritch blasts.

For the sake of visualisation:

D--S--B

Which of these three possibilities happen?

1. The skeleton moves to Boris's side due to the repelling blast and
   gets an attack of opportunity on Boris when he casts eldritch blast.


2. The skeleton simply keeps its position.


3. The skeleton takes damage as if it fell 20 feet due to the crushing
   force. (With 10 feet of a push from either side)

The skeleton may be moved twice; no falling damage

It moves twice if each blast successfully rolls "to hit" which would leave the skeleton in its original position at the end of Doris' turn (possibly destroyed). It is worth noting that the trigger to Boris' attack is Doris' attack, so Doris' turn is "when it all happens>."

When the trigger occurs, you can either take your reaction right after
the trigger finishes or ignore the trigger. (Ready Action, Basic
Rules, p. 75)

1. 
   

   There is no opportunity attack made on Boris. Boris didn't move out of the skeleton's reach. (This isn't 3.x edition)

   
   
   

   
   

   If you leave a hostile creature’s reach during your move, you provoke an opportunity attack (Basic Rules, p. 73)

   
   

   
   


2. 
   

   Doris' blast moves the skeleton one way (on a hit) and then Boris' blast moves it back the other way (on a hit).

   
   
   

   If either Boris or Doris miss, the skeleton moves in one direction. If they both miss, hilarity ensues and the skeleton keeps on grinning.

   
   


3. 
   

   There is no fall, and thus no falling damage, for being moved laterally.

   
   
   

   
   

   A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for
   every 10 feet it fell, to a maximum of 20d6. (Basic Rules, p. 68)

   
   

   
   
   

   The Combined damage of two eldritch blasts (2d10) may kill the skeleton anyway, so it would be fun to narrate it as being shattered by the opposed effects if the damage is enough to destroy it.

   
   

Rule of Cool

If both eldritch blasts hit, the DM can invoke the rule of cool and apply some bludgeoning damage to the skeleton. Even though, by the way action/ready action works, Doris' blast would likely hit first¹ -- maybe it takes a DC 16 Dexterity check to get the timing just right? -- the DM rewarding the two players for cool innovation is consistent with Rules As Fun.

¹ If using the optional rule in Xanathar's Guide to Everything, it could be simultaneous, if Doris so chooses:

If two or more things happen at the same time on a character or
monster's turn, the person at the game table - whether player or DM -
who controls that creature decides the order in which those things
happen. For example, if two effects occur at the end of a player
character's turn, the player decides which of the two effects happens
first.

Two Eldritch Blasts will not combine to do extra damage.

No Opportunity Attacks

None for the characters

Being pushed by repelling blasts does not provoke opportunity attacks:

You also don't provoke an opportunity attack when you teleport or when someone or something moves you without using your movement, action, or reaction. For example, you don't provoke an opportunity attack if an explosion hurls you out of a foe's reach or if gravity causes you to fall past an enemy.

None for the skeleton

Attacks of Opportunity are triggered when an enemy moves out of your reach. Not when you are moved out of the enemy's reach.

You can make an opportunity attack when a hostile creature that you can see moves out of your reach.

No Crushing Damage

Spells do what they say they do. Both blasts do the damage and effect they would normally do. Nothing in their description affords extra damage due to crushing. There aren't any rules regarding crushing damage from being pushed. Damage resulting from such things need to be specified in the description of the ability or effect that does the damage.

Skeleton is pushed one way then the other

In the example posted, the order the skeleton is pushed follows the initiative order. In the event that one or both blasts were triggered "at the same time" due to a held action, the person who's turn it is decides the order in which the effects occur.

Per Xanathar's Guide to Everything:

If two or more things happen at the same time on a character or monster's turn, the person at the game table - whether player or DM - who controls that creature decides the order in which those things happen. For example, if two effects occur at the end of a player character's turn, the player decides which of the two effects happens first.

4. None of the Above (But 1 & 2 are partly correct)

Strictly speaking, in 5th edition D&D, nothing is simultaneous. If two events are simultaneous, they'll be resolved in some kind of order, as specified by

• the DM, or


• the affected Player, or


• the spell's rules

... Depending on the circumstances.

In this situation, if both Boris and Doris both attempt to cast Eldritch Blast on their target at the same time, using Readied Actions, the DM will need to decide which happens first. A common way for the DM to rule is to use their previously decided initiative order to determine their order of execution.

The skeleton will be in the same position (if both blasts resolve with the same number of hits)

The skeleton is getting pushed in someone's direction first before being pushed in the other direction, but assuming both blasts hit (the same number of times), the skeleton will first be pushed in one direction, then back to its original position.

No Attacks of Opportunity

Attacks of Opportunity occur only on voluntary movement, not involuntary movement. Pushing a skeleton around will trigger Attacks of Opportunity for neither player, nor the skeleton itself, nor any other creatures that might be within melee range of any of the skeleton's positions.

No Damage (other than the normal damage dealt by Eldritch Blast)

Spells only do what they say they do, so without Eldritch Blast or Repelling Blast saying anything about their ability to deal damage through their movement, this "crushing effect" cannot cause damage to the skeleton. A permissive DM might choose to rule that damage happens, but that would not be RAW.

By RAW, nothing of the sort happens. This is ok, because you aren't using the cantrips as written; instead, you are trying to stunt.

Stunts are adjucated by the DM in every version of D&D.

Here

1. Your trick is specific to the target (a creature vulnerable to Bludgeoning damage)




2. Your trick requires non-trivial positioning (each of you on either side of your target, making a ranged attack; like flanking)




3. Your trick uses nothing in the environment.




4. Your trick is repeatable otherwise.

A DM might offer advantage, or change the damage type of the blasts to Bludgeoning if both hit (while losing the push), or both. Or neither.

Stunting has a long history in D&D and RPGs in general. There are no rules for stunting in 5e other than "ask your DM". The prior version of D&D, 4e, had a table on page 42 to help the DM determine what effect a creative stunt should have; 5e didn't duplicate that table.