A speaker says, "I like red". Here are a few of the many things they could mean[1] by that. 

1. I like red.
2. I want you to believe that I like red.
3. I want myself to believe that I like red, and this can be assisted by a public statement.
4. I think that the community valence of red should be higher. I’m ready to defend this position if sufficiently provoked, but this will be a battle for both parties, so I don’t recommend attacking it unless you are very confident in your position.
5. I want to hint that I like Communism, but for various reasons I feel uncomfortable saying that more plainly.
6. You should associate me with the cool people (who like red).
7. I’ve recognized that you identify with liking red. As such, I want to express my commitment to support you.
8. Due to incentives related to (7), our culture has internalized norms around people professing likes for things unique to specific tribes. When I say "I like red", I'm showing that I respect these norms, even though none of us might understand the origins or purposes of these norms.
9. I’m sure you recognize that by all accounts I should probably hate red. But I know that liking it would be more convenient for your situation. This discrepancy makes my saying a more clear signal of loyalty.
10. I’ve recognized that group X is associated with the liking or disliking of redness, and would like to express my loyalties accordingly. This will help craft very specific alliances, though at the possible expense of making some enemies.
11. I recognized that you've developed a positive connotation towards people who do (10). I'd like to position myself with these people, even though I don't understand the background context.
12. (Related to 11): Fred from accounting says "I like red" a lot, and he's successful. I might as well say it and hope for the best.
13. I just want you to know that I’m talking to you, the particular information doesn’t matter much. This could be useful to signal that I'm willing to be social, and/or that I see you as a friend/colleague/potential partner.

A listener might pick up that intended meaning, or they might learn different things than the speaker intended. These could include:

B1. I have background knowledge that people who like red are overwhelming represented by tribe Y, which have characteristics M and K, so I can infer that the speaker has characteristics M and K.

B2. The speaker thinks they like red. However, I can be confident that they have a really confused or overgeneralized definition of red, and haven’t thought about it very hard.

B3. Null. The costs of interpreting and remembering this phrase exceed the expected benefits, so it's being ignored.

B4. Null. I've already been able to predict with 100% accuracy that the speaker would say "I like red", so this gives me zero new information.

B5. I was expecting the speaker to say something more relevant in their own father’s eulogy. I’m going to infer that they are pretty naive about social environments. 

Additional suggestions of meanings are appreciated. (Leave as comments)

With more reflection, one could likely come up with a possible context such that "I like red" could mean any other statement, though most of the options would be trivial. Perhaps this process of trying to list interesting potential meanings and interpretations is futile, because the space is too large and ill-defined. However, my hunch is that there are some interesting subgroups, most of which are presented above in some shape.

Reflections

I think these sorts of meanings are very common. There are three obvious reasons for such meanings:

1. Communication is expensive, so we compress it a whole lot. Sometimes context fills in the gap, but often it doesn't completely fill it in. This means that we often lose clarity, even when we would prefer otherwise.
2. In many situations, vagueness, ambiguity, or dog-whistling (sending information very particularly with a subgroup who you believe is likely to actually understand it) are preferable or necessary.
3. Communication isn't always deliberate. People either subconsiously lean towards communication with coded meanings that they think might be advantageous to them, or they repeat internalized patterns that they don't understand (but predict will be advantageous).

Implications

In the post on Implicature Conflation, abramdemski suggests that people "simply stop equivocating." If taken at face value, I'm not sure I totally agree. However, I do think that communication styles that come with vagueness and multiple levels of meta, represent significant costs. I imagine that we generally want to encourage more plain communication, but I expect that this desire will take extended effort for long periods of time to make progress on.

I would like to see better categorization/ontology of these sorts of communication. The Simulacrum Levels seem too simple (only 4 linear levels) and opaque.

Related discussion

Simulacrum Levels 

Much of this is related to the concept of Simulacrum Levels. I think (1) is at Simulacrum level 1, (2) is at Simulacrum level 2, (5, 7, and 10) with Simulacrum level 3, and maybe (8,11,12) with Simulacrum level 4. I'm really unsure about this though, I find the levels confusing.

Conversational Implicature

As abramdemski wrote, 

In case you're not familiar with the term, "conversational implicature" refers to all the meaning that's not explicit. For example, if I say "you didn't do the laundry yet?" I might (depending on context) be implying "you should really do it now". This is implicature, because I didn't say it explicitly; it is inferred from context.

Arguably, almost all of these examples are about information that's not explicit, so might count as conversational implicature.

Ask vs. guess culture

Relevant post here. Guess culture requires more interpretation of things; it has more implicature.

Language Games

I believe some of the work on implicature was inspired by Wittgenstien's work around language games. My impression is that the newer work is better developed (though not as developed as I'd like) but it might be useful to point out the history.

[1]: Here, mean roughly means "attempt to convey" or "reason for saying"