Show them. :) It's always best to lead by example. Have your Non-player characters use specific references and attitudes that can be easily copied -- however clumsily at first! -- and keep on hammering them with good examples until they get the hang of it.
If and when players lapse into American-speak or other characteristics you don't want to encourage, again rely on your NPCs. Have them misunderstand, react poorly to innocent comments, and provide other negative reinforcement (tho as little as necessary) to illustrate the worst-case scenario.
As noted in other responses here, reward it when they try. Keep the rewards small at first, but specify clearly exactly how much they're getting for which comments, attitudes, and actions. Then increase the rewards in response to more and better attempts. Next thing you know you'll have started a trend... and the better players of such roles will be getting bigger and better rewards. They'll keep leading by example, taking a lot of the load off your shoulders.
Finally, find written works (if you can) that can supply both ideas and one-liners that can be used or copied by the players. Such things will vary widely by setting and culture, else I'd recommend specific examples.
Best of luck!
OK, I don't have time to answer this as I want to. My background is in psychology, and I fell into role playing games when I turned 10 in 1976. So by the time I was in college, understanding where the term Roleplaying game really came from, I understood the critical nature of immersion, how it is the most important ingredient for game success.
And to be clear, the definition of immersion is to "Immerse oneself into the identity and Role of the part one is playing. To respond, as much as possible, as the person one is playing, not as oneself."
And before getting into the smaller details, I will dive right into the fact that the very system/game one chooses has a huge amount to do with the amount of Immersion.
Metagaming is the opposite of immersion. You use both terms, but I need to make that absolute definition from the beginning. This also means rules that encourage metagaming decrease the immersion in a game and therefore, decrease the main ingredient of a roleplaying game. The mechanics are called "Dissociated Mechanics", a term coined by Justin Alexander. This is very worth reading, because it gets into many of the larger picture issues with players being able to use in-game logic to see the world around them, as opposed to the rules forcing dissociation from in-game logic.
Once the players assume that rules are going to determine the content of an encounter or treasure (based on EL, or whatever) instead of what the environment or history of the area dictate, verisimilitude is lost.
Vreeg's Rules of Setting design are also heavily immersion related. My current campaign is 26 or so years old (started in '83). Building verisimilitude is a huge part of this.
Vreeg's first Rule of Setting Design
Make sure the ruleset you are using
matches the setting and game you want
to play, because the setting and game
WILL eventually match the system.
Corollary to Vreeg's First Rule
The proportion of rules given to a
certain dimension of an RPG partially
dictate what kind of game the rules
will create. If 80% of the rulebook
is written about thieves and the
underworld, the game that is meant
for is thieving. If 80% of the
mechanics are based on combat, the
game will revolve around combat.
- Multiply this by 10 if the reward
system is based in the same area as
the preponderance of rules.
2nd Corollary
Character growth is
the greatest reinforcer. The
synthesis of pride in achievement
with improvement in the character
provides over 50% of the
reinforcement in playing the game.
Rules that involve these factors are
the most powerful in the game.
Vreeg’s Second Rule of Setting Design
Consistency is the
Handmaiden of Immersion and
Verisimilitude. Keep good notes, and
spend a little time after every
creation to ‘connect the dots’. If
you create a foodstuff or drink, make
sure you note whether the bars or inns
the players frequent stock it. Is it made
locally, or is it imported? If so,
where from? If locally made, is it
exported?
Vreeg's Third Rule of Setting Design
The World In Motion is critical
for Immersion, so create 'event
chains' that happen at all levels of
design. The players need to feel like
things will happen with or without
them; they need to feel like they can
affect the outcome, but event-chains
need velocity, not just speed.
Vreeg's Fourth Rule of Setting Design
Create motivated events and
NPCs, this will invariably create
motivated PCs. Things are not just
happening, they happen because they
matter to people (NPCs). There is no
need to overact, just make sure that the
settings and event-chains are
motivated and that the PCs feel
this.
Vreeg's Fifth Rule of Setting Design
The Illusion of Preparedness is critical
for immersion; allowing the players to see
where things are improvised or changed
reminds them to think outside the setting,
removing them forcibly from immersion.
Whenever the players can see the hand of the GM - even when the GM needs to change things in their favor -
it removes them from the immersed position.
(Cole, of the RPGsite, gets credit for the term).
Remember that part of immersion is the lack of feeling walls around and rails under the characters. This means that the players should not feel that there are things that their character cannot do solely because of the rules or the GM's mindset. The job of the GM is to enable roleplay, not to inhibit it.
This also means the GM must be as immersed as the players, or more.
Another big-picture thing that may irk some folk who sell stuff is that published settings can hurt immersion. They don't destroy it; but when the players have a lot of knowledge about a setting that their character would not have, this increases the opportunity to use it, consciously or unconsciously. Similarly, if your setting has its own bestiary that the characters learn as they go along, or at least a lot of homebrew tweaks, the players get used to working with the in-house data and not trusting the published sources.
If you have done all of this larger-scope stuff, the smaller scope stuff becomes easier. As a GM with miles on the tires, I find that playing up the level of knowledge my NPCs might have and do not have helps keep the players in the same mindset. Players key heavily off the way the GM plays their NPCs. They won't do the funny voices or the mannerisms if the GM does not, and if the GM is particularly careful about what their NPCs know and don't know, especially verbally, the players emulate this.
Best Answer
1. Communicate your expectations with the players out of game
You and your players seem to have different expectations for how their character sheet should influence their roleplay. To you, it's immersion-breaking when a character acts differently than what their ability score suggests. To others, ability scores are just numbers that define mechanics and statistical outcomes, and don't directly restrict roleplay style.
It would benefit your campaign if you held an out-of-game discussion to directly address your roleplaying expectations and concerns. Discuss how you think characters should behave if their Intelligence, Wisdom, or Charisma is notably high or low. Get feedback. Make sure your players' preferences are in sync with yours.
Note that it may be an uphill battle if your players disagree. While a PC's ability scores affect what tasks they can do and their likelihood of success, they don't dictate roleplay or how the player should act out the character's thoughts and choices. Strictly speaking, it's the player's choice whether or not the PC's mental ability scores affect their roleplay, and to what degree. Assuming they wrote the character, they probably know best how the character would act and behave.
2. Use checks when players roleplay differently from their ability scores
If you want the ability scores to matter more, then include more dice-based challenges. This is where you have the system mechanics on your side. Characters with low WIS are less likely to succeed an WIS-demanding task. You can also prompt players to make checks, and then you can intervene regarding their character based on their success or failure on the check.
For example, if a player forgets or misses a clue but their character has high INT, have them make an INT check. On a success, they get a reminder or hint from the GM.
These checks can also be used (albeit sparingly) when players roleplay above their PC's capabilities. If the low-CHA character delivers an eloquent speech, ask them to make a CHA check or related skill. On a failure, you narrate that the audience wasn't particularly moved.
When intervening this way, make sure to use the “Yes, and” style of narration. Yes, the high-WIS druid walks toward the spider cave, and then has a flash of insight and realizes it's a bad idea. Yes, the low-CHA barbarian tries to speak politely and articulately, and the duke dislikes their untidy appearance and finds the speech unsettling. This way you still respect player agency, while maintaining narrative flow and nudging them to act more in-character.
3. Give in-game rewards for good roleplaying
Another way to encourage players is to give in-game incentives. Avoid big rewards like bonus XP, because that can seem unfair and subjective; from my experience, GMs who give roleplaying XP may seem biased toward certain players, which quickly results in player frustration. Also avoid punishing players for what you consider bad roleplaying. Accusing players of bad roleplay when they are putting effort into roleplay could discourage them from roleplaying at all.
Instead, reward players for roleplaying in character and maintaining immersion. Use small rewards, like a temporary circumstance bonus for roleplaying in accordance with the ability score. This could encourage players to roleplay having low stats. They're already disadvantaged mechanically, and a temporary bonus would increase their odds of success.