Using "curious" in the sense of "odd" or "strange" is more British than American. It does still crop up here and there, but is somewhat archaic, formal -- or, in fiction, intended to convey a British and/or old-fashioned kind of person. E.g., 'How curious!' Dorothy said, peering at the bright purple tree.
So absent context, "The curious boy" will be ambiguous. No getting around it. You have to tell whether it's about the boy investigating something ("The curious boy pressed deeper into the forest") or about a boy being odd in some way ("The curious boy walked down the sidewalk, and we all stared at him"). Or if it means both!
This ambiguity will also be used when someone wants to make puns. "What a curious creature you are!" may mean "you are always wanting to investigate" or it may mean "odd." I recall there being some of this double-meaning in Alice in Wonderland.
"He's very curious" will generally be understood to mean someone has the quality of curiosity, not oddness, in modern American English, but if you want to reduce ambiguity, you use "about" to clarify. "He's very curious about everything!" "She's very curious about ancient Egypt." "The neighbors very curious about our business, and I want better curtains in our house!"
In modern American, "curious" people or animals (the curious cat, the curious child) will be "inquisitive" with an ambiguous side-order of "odd"; the more stereotypically inquisitive the animal (or person: the curious neighbor), the more likely the assumption will swing to "inquisitive." But "curious" inanimate objects will always be "odd." And "a curiosity" is an odd thing.
(You wouldn't use "Curious you!" because either way, applying adjectives to pronouns rarely works well. "Red you!" "Angry him!" "Stinky her!" "Inquisitive me!" -- you can get away with it sometimes, in a slangy fashion, but you tend to need a noun, like "Curious George," the monkey who is curious about everything! (The Curious George books are a series of children's books which strongly normalizes "curious" as an adjective meaning "inquisitive.")
So if you want to avoid ambiguity, use "odd" or "peculiar" or "weird" or "fascinating" in American English, to mean those things. And only use "curious" for things like "He's very curious" (inquisitive) or "I'm curious about this sentence here" (I want to understand this sentence better, I am interested in this sentence).
In the etymology you've posted, 'fun' is described as "to cheat, hoax" as early as the 1680s. 'Funny' is then attested at a later time as a modifier with a slightly modified sense emphasizing the humorous aspect of something like a hoax or joke. A particular 'cheat', 'trick', or 'hoax' could seem more like a good-natured laugh or more like a mean-spirited attack. You see this spectrum of meanings in the various definitions.
At it's core, 'funny' means 'unusual', 'unexpected', or 'odd'. All the definitions you've included in your questions are just different, more specific ways in which it is used to mean this.
Humorous
Things which are completely expected, known, and ordinary are generally not funny. Most humor involves misdirection and surprise, so it fits in with the ideas of unusual and unexpected, i.e. 'odd'.
Strange
I hope this is clear.
Dishonest
Things or people which are dishonest are not what they're expected or believed to be. Some uses of 'funny' in this sense include "funny money" and "funny business".
Unfriendly
I'm not familiar with this usage, but I'm not from the UK. The closest thing I can think of is "you're acting funny" when someone seems to be offended. This is said because the person is not acting in their usual manner, but instead in an offended manner. I suppose this could be extended to general unfriendliness fairly easily.
Ill
The important thing to note here is that 'funny' can mean "slightly ill". Feeling funny is between feeling healthy and feeling sick. You don't feel like you normally do, but you don't feel awful either. A simple stomach ache probably doesn't go beyond feeling funny, but the flu takes you all the way to sick.
A synonym for this sense of 'funny' would be 'quesy'.
Crazy
Crazy things are so unexpected and unusual that we often can't figure out why they would be that way.
Best Answer
I can understand why the connection between these two senses of "dispose" seems so mysterious. The key to understanding it is: "to get rid of" is actually a secondary sense, even though today it is very common. The primary sense is "to put things into their proper places". The primary sense is now rare, but it still colors and explains the secondary senses.
Putting things into their proper place
When you dispose of garbage, you put it into its proper place: a garbage can, the city dump, or someplace like that. When you dispose of radioactive waste, you put it someplace very far away from people. However, throwing away garbage is only one of many ways that things can be "disposed of".
Here, "dispose of" doesn't mean "get rid of" those resources, it means to put them to work in a coordinated manner—that is, to bring them to the proper places for performing some large, coordinated action.
In the Order Disposal Problem:
the word "dispose" means "to complete a job"—another way in which something can be put into its settled and proper place.
Being ready to act
Here is an example of saying that someone is disposed to act in a certain way:
This calls upon another secondary sense of dispose: to put into a state of readiness to do some action—the action that one is disposed to or toward. The elements of one's mind, one's habits, one's abilities, one's resources, one's knowledge, one's surroundings, etc. are in a configuration that makes one especially ready to perform the action. This sense also occurs in sentences like this:
Figuring out more senses of dispose
The word "dispose" gets used for many, widely varying meanings—more than I can list here, and indeed more than you'll find in dictionaries. Once you understand the primary meaning, it becomes a lot easier to understand how people are extending that meaning to fit different situations.
I think it helps to know the etymology, both for understanding the many senses of "dispose" and for many other words that contain the same two roots: dis- and pose. "Dis-" (in "dispose") is a Latin root meaning to break apart and spread out, as in disperse, disseminate, dissolve. "Pose" is a Latin root meaning to put something in a certain place or state, as in position, opposite, repose.
Knowing that, you might be able to figure out that a disposition can mean both an inclination toward doing something and the result of doing something—"where" things ultimately got put. The latter sense is rare, but an example is that in computers, a task is sometimes said to have a "disposition" of succeeded/failed/aborted. Another one is:
This means that I can bring five employees to the appropriate place, where they will be ready to do as you command.
And finally, here's a stock phrase which is worth knowing, because it sheds a lot of light on the other senses: propose and dispose. Here's an example:
This means that men offer possibilities to consider (propose), and women decide which proposals to carry out and which to reject (dispose—that is, sort out the proposals and bring some but not all to action).