None of them are grammatical full sentences, if we don't consider "why so" as having a meaning of its own. And we'll do that in a minute, but let's first pretend that it doesn't have one.
Possible full sentences would be:
Why are you so sure?
How are you so sure?
Why is it that you are so sure?
How is it that you are so sure?
The forms you all have are eliding part of these sentences.
Now, those that do not contain so could be construed as elisions from different questions; asking why someone is sure of something is different to to asking why they are sure to the extent that they are. Of course, we could be asking that, but that's not the form that has become idiomatic, as we'll come to.
The way elision works with contexts is complicated, in that we can understand e.g. some headlines fine that we'd trip up on in the middle of a passage of prose.
And similarly, while "how so sure?" doesn't scan right, we still understand it, and it would unusual, but not utterly bizarre, for someone to use it in informal speech.
Likewise with "why so sure?" except that "why so" has been used so much as to become an idiom of its own, indeed one that is defined in its own right in at least one dictionary.
And so, after that little journey through elision, we can see that because "why so" has been so often used as to become an idiom, we can actually understand "why so sure" without reference to elision at all, but in terms of that idiomatic meaning.
("Why so" was once also used as an expression of relief or acquiescence, as it is used by Shakespeare and continued to be used into the 19th Century, this other meaning might or might not have helped "why so" in the sense here come into being).
"How so" has had a different journey toward becoming an idiom, in that it is often found as the entirety of a question ("How so?"). As such, just as we can understand "why so X?" as an idiomatic form with a defined meaning, so we can "how so?", but not "why so?" or "how so X?" because that is not what those idioms mean.
According to Wiktionary, the adjective grammatical means:
(linguistics) Acceptable as a correct sentence or clause as determined
by the rules and conventions of the grammar, or morpho-syntax of the
language.
In the linked related question, Can “grammatical” mean “grammatically correct”?, Berrie England wrote:
To say that a sentence is grammatical is to say that it conforms to
the rules of English grammar as found in the way in which native
speakers normally use the language and... Describing any construction as incorrect is unhelpful and inadequate. That is why, in most cases, it it makes more sense simply to say whether or not a construction is grammatical.
I have seen some occasions where there are two different explanations about a grammatical issue. For example, the linked question “The earthquake, along with its subsequent aftershocks, HAS/HAVE …” asks whether it is grammatical to use have or has after "The earthquake, along with its subsequent aftershocks..."
There are two distinctly different answers posted by two users, one says we have to use has as the earthquake is the subject and along with... is a prepositional phrase, and the other says has is right, but we could consider using have as along with... has a potential to be considered as a conjunction.
Which is grammatically correct? Both of them are grammatical as long as you could quote the right reference in a grammar book.
Should we use are or is after dummy there when there are plural words following the verb? Should we use are or is after a collective noun such as family, team, etc. Can we use an indefinite article before a mass noun? Should all the English adjectives be placed before a noun? How about something special?
There are countless number of grammatical questions that could be answered in more than two ways. And some say A is grammatically correct, but B is broadly used colloquially.
What does colloquially exactly mean, then? Does it mean it is not grammatical?
I would have called you if you would have let me know it was that
urgent.
Is the above sentence grammatical? Related question, “If I would have lost you” vs “If I had lost you”.
The answer is no. But it is used colloquially by some people especially in the U.S.
If A writes a grammar book that says we can use would have + PP after the conjunction if, the above sentence would be grammatical in accordance with the grammar book written by A, but it would be ungrammatical according to B, C, D, etc.
But we can't always say which book or grammar you are referring to when you say some sentences or clauses are grammatical, then, the word is as ambiguous as it gets and should be avoided unless you are sure about which grammar book you are referring to.
I think grammatical is often times synonymous with "it makes sense to my native ears" and it could be used when you talk about uncontroversial rules that are so obvious that you don't have to quote any grammar book. But saying it is grammatical should be avoided when you are not sure about what grammar rules you are referring to.
Best Answer
Say is a bitransitive verb, which means it takes two object phrases.
One is the person addressed (the Indirect Object), and the other is what was said (the Direct Object).
Most bitransitive verbs govern the Dative Alternation. This means that the two objects can appear in two different orders, ad lib, without any meaning difference. In one variant, the Indirect Object appears with a preposition to; in the other the order is reversed and there is no preposition.
Subject
-Verb
-Direct Object
- toIndirect Object
but these are not grammatical:
or
Subject
-Verb
-Indirect Object
-Direct Object
but these are not grammatical:
However, say does not govern the Dative Alternation (although tell does -- that's one of the differences between them), and therefore the first alternant is the only way that both objects can appear with say. Thus it's ungrammatical to say