From the Player's Basic Rules, page 71 (or PHB p. 191):
In contrast, you can move through a hostile creature's space only if the creature is two sizes larger or two sizes smaller than you.
An ogre is a large creature and elves are medium. So an ogre can't move through an elf's space. In your previous example, if we have a 10-foot wide passageway with two elves standing side by side, the ogre can't get through without killing one of the elves or forcing them to move.
The rules on squeezing into a smaller space are for an ogre trying to move along a 5 foot corridor. The rules on creature size that you've quoted back this up—the ogre isn't actually 10 feet wide, that's just the space he controls. So he can move through a 5 foot wide gap, but it's cramped and he can't move freely.
Now, you might be thinking that it's a bit unfair on the ogre if the 2 elves can form an impenetrable barrier against it. As you've said, he'd rather shove them aside than squeeze between them. And he can do just that! From the Player's Basic Rules, page 74:
Using the Attack action, you can make a special melee attack to shove a creature, either to knock it prone or push it away from you. If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
The target of your shove must be no more than one size larger than you, and it must be within your reach. You must make a Strength(Athletics) check contested by the target's Strength(Athletics) or Dexterity(Acrobatics) check (the target chooses the ability to use). If you win the contest, you either knock the target prone or push it 5 feet away from you.
So you're right, shoving is the ogre's answer here.
Now, with your new example, (2 elves in a 15 foot corridor with a 5 foot gape between them), things are different. The ogre does indeed have to squeeze between them. Fortunately for him, it's not going to matter all that much.
Why? Because he's almost guaranteed to be moving on his own turn. Unless there are more enemies than just the elves, he's not going to provoke any opportunity attacks while squeezing, and he can attack before or after he squeezes. So the only squeezing penalty that is actually going to apply to him in this situation is the double cost for movement.
Note that if he stopped between the elves, all these penalties would apply to him. That makes sense though—standing between two enemies with not enough space to move around in would make it difficult to dodge attacks or attack effectively.
Space doesn't only mean the area you physically inhabit in combat
An ogre isn't 10 feet tall by 10 feet wide, they simply command a 10 X 10 combat square area. It would have a penalty to Dex moving through a 5 foot wide square because it can't effectively dodge when the walls are brushing up on it's sides.
This is the same for Medium and Small creatures, who command a 5 X 5 square. They don't command that area because they're that big, they command it because they're actively engaged in combat inside of it and moving within it.
Basically, you've equated combat squares with obstacles to movement in general.
For example: A space large enough for a medium creature to move freely through would be a standard door. However an ogre would need to squeeze through because they're wider and taller than a standard door.
So when you're looking at a medium creature squeezing through a small creatures opening, it's akin to an average person trying to move through a crawl space. While the small creature would be able to do it easily, the medium creature would need to squeeze.
For example, I ran a game with a bunch of small creatures pestering the party and retreating to bolt holes with an opening that would only accommodate small creatures. That means the opening isn't 5 feet wide. By squeezing rules, a party member of medium size could have traversed the tunnels, albeit slowly and at significant disadvantage. Whereas the enemies could freely move and attack using the tunnels for cover and being an extreme and persistent annoyance.
Best Answer
Don't get tangled in the particular abstractions
Your intention is to block a corridor, about three metres wide, by standing in the middle (and presumable striking or tripping or blocking opponents as they come?). Clearly this is a reasonable thing to try. Now, the group, probably with the game master in charge, has to figure out how to represent this within rules framework in use.
Maybe you are preparing to attack or push anyone trying to pass you (ready an action)? This work regardless of the particulars of the grid in use. Just do it.
Is it credible that just by standing over there there is not enough space for others to get past? Three meters is quite wide, so unless you have an almost three meter wide barrier with you, quite unlikely. But three meters is narrow enough that enemies can't get past you without worrying, especially if you are in the middle. The game represents this in a somewhat strange way by opportunity attacks. Use them (or house rule if they do not satisfy your group).
If, for some reason, it is vitally important that you are in fact standing right in the middle of the corridor, and it is vitally important to use a grid here and now, consider the following alternatives:
Align the grid so that one grid is in the middle. The corridor can be diagonal.
Align the grid so that one grid is in the middle. The corridor can consist of half-squares.
Use a hexagonal grid instead and place it so that a hex is in the desired position in the middle of the corridor.
In any of these cases, you might want to have to adjudicate things such as partial squares or hexes.
So it might be easier to ignore the grid for a while or to just assume that there is a small local change in the grid which allows someone to stand in the middle, but still so that only two people can fight side by side in the corridor (when someone comes to one side, their attacks force you to take a step to the other, so that both are located in a definite square). And if an area of effect would hit precisely one of those squares and you are in the liminal stage between them, roll d2 to see if you are affected or roll your saving throw with advantage or take only half damage, whichever suits the situation best.
Summarizing: Use the rules to model the current fictional situation in a satisfactory way, rather than taking the abstraction the rules cover as a ground truth.