As a GM, I avoid directly telling players things like a monster's CR and instead get creative with how I describe them. A lich? "Despite looking like a withered old man, he's surrounded by a sinister aura, and when your eyes meet his, a chill runs down your spine as he looks at you like something he found on the bottom of his shoe." A marilith? "The snake-like monster feels... wrong. After observing it for a while, you come to realize that there's something deeply disturbing about the way it moves and you can detect a faint scent of brimstone surrounding it." (well, brimstone is more associated with hell and devils, but I hope you get the idea)

If you consistently apply descriptions like these to powerful monsters, your players should get the hint.

Insightful Manipulator

Depending what you want to know, a Mastermind Rogue obtains a feature at level 9 called Insightful Manipulator (XGtE, p. 46):

Starting at 9th level, if you spend at least 1 minute observing or interacting with another creature outside combat, you can learn certain information about its capabilities compared to your own. The DM tells you if the creature is your equal, superior, or inferior in regard to two of the following characteristics of your choice:

• Intelligence score
• Wisdom score
• Charisma score
• Class levels (if any)

At the DM's option, you might also realize you know a piece of the creature's history or one of its personality traits, if it has any.

This might be very useful information in combat, e.g. for spellcasters. It requires interaction outside combat though, which tends to make the Mastermind Rogue quite the... talkative type.

Aside from a few class features, it is very table-dependent

A Battlemaster Fighter, at level 7, can

spend at least 1 minute observing or interacting with another creature outside combat [to] learn certain information about its capabilities compared to your own.

A Mastermind Rogue, at level 9, can

spend at least 1 minute observing or interacting with another creature outside combat [to] learn certain information about its capabilities compared to your own.

That being said, I agree with you, PCs living in this world should know how to evaluate someone's relative strength. There are many ways of doing this, and they can vary wildly at each table. Here are some of my uses.

• HP information. I tend to describe HP loss to my players. The DMG lists a few examples.

  When you drop below half your hit point maximum, you show signs of wear, such as cuts and bruises. An attack that reduces you to O hit points strikes you directly, leaving a bleeding injury or other trauma, or it simply knocks you unconscious.

• Description. Sometimes, just narrating the effect a monster has on the party is sufficient.

  As this creature moves, each step shakes the ground. Even Kalluz, the Barbarian, is feeling his heart's accelerating rhythm. When it finally emerges from the mist, you see a gigantic lizard. The Wizard recalls this ancient creature's name, a Tyrannosaurus Rex. Standing 3 or 4 times larger than you, it roars at you, and the very trees around you seem to bend slightly.

• Looks. I show my players the MM images of monsters. This instantly provides some obvious information, such as whether the monster hovers or not, how effective could a Blind effect be, etc.

• Intelligence checks. Players ask if their PCs have ever heard about some creature. Religion checks provide information of Celestials, Fiends, Demons, etc; Nature checks for beasts and humanoids; History for legendary creatures; Arcana for inhabitants of magical planes.

• Investigation checks. Players can use their action to learn basic information about the creature. Whether it looks like it attacks with Strength or Dexterity. Whether it attacks at a range or within melee. Whether it looks fast or not. Whether it looks like a standard challenge or a deadly one for the party. I avoid giving information that would overshadow the "Know Your Enemy" feature.

• Passive intelligence checks. I'm aware my Wizard has +8 in all Intelligence checks apart from History, so I offer him some information even if he doesn't request it. On his turn, he often shares advice with the party:

  Don't go near him, he is weak at a distance!

Know Your Enemy

The "Know Your Enemy" Battle Master Fighter feature (PHB, pp. 73-74) does exactly that:

The DM tells you if the creature is your equal, superior, or inferior in regard to two of the following characteristics of your choice:

• Strength score
• Dexterity score
• Constitution score
• Armor Class
• Current hit points
• Total class levels (if any)
• Fighter class levels (if any)

However, the question premise is a bit flawed

Certain skill checks in DnD, like Nature or Religion, allow PCs to learn bits of lore or narrative information

That is not exactly true. There are no skill checks in 5th edition. Using particular skills in order to achieve some expected goal was the 3.x thing. It is not the way how 5e is supposed to work.

Instead, players describe, what do their characters do. So a player just asks you "I observe a monster for a while. Do I understand, how dangerous it is?" As a DM you might (or might not) ask a player for an ability check before resolving the outcome. Revealing a particular creature's stats is a decision that is completely up to the DM.

how can I let my players know the power gap between them and the other creatures?

If you are the DM, it's your concern to give players information that is relevant, reasonable and accessible. Read a couple of relevant questions:

• How do I help my players figure out how to stay alive in a realistically-deadly sandbox campaign?
• How can I tell how powerful an NPC is without being explicitly told?

Mechanics knowledge is table-dependent

in a game as combat-oriented as DnD, knowing an opponent’s stats, or at least how they relate to yours, is vital to make an informed decision

That's true. This is the reason, why some DMs explicitly reveals monsters stats. There is nothing wrong with it. While DMG suggests a few ways of conveying remaining hit points, it also mentions that a DM can say the number explicitly. The same is true for other stats, and table-dependent as well, see Are enemies' combat statistics and current HP public or hidden?

See also Does D&D 5e have a rule for character knowledge about monsters?