If and Whether - or not? Interrogative and Conditional words

It's clear to me that in some situations, "if" works but "whether" does not: 1a) If it rains, I shall take my umbrella. 1b) Call me if rain is predicted.

Also some where only "whether or not" will work: 2a) Whether or not it rains, I still have to go to work.

and some where only "whether" works: 2b) Whether you like this example is of no concern to me.

According to Grammar Girl, there are sitiations where the "or not" is superfluous, as it's not needed to clarify the meaning. 3a) Let me know whether you're going. 3b) Let me know whether or not you're going.

There are also situations where any of the three constructions would work, but the meaning is different:

4a) Let me know if rain is predicted. 4b) Let me know whether rain is predicted. 4c) Let me know whether rain is predicted or not. (to me, 4c above seems ambiguous as to what the speaker wants to know—the prediction or something else altogether— so it needs more context to clarify that)

Can someone succinctly explain which rules of grammar or syntax are operative in these examples, and whether there are other situations where other rules might apply for "if" VS "whether" VS "whether or not"?

Also, are there recognized differences in formal and casual usage?

Conditionals

Whether or not and if can both be used in conditionals:

• Whether or not it rains, I'm going to the park.
• If it rains I'm going to the park.

Notice though that the meanings are very different. In the first sentence I am definitely going to the park - whatever happens. However, in the second sentence, I may not be going to the park if it doesn't rain.

Whether on its own cannot be used in conditionals:

• *Whether it rains, I'm going to the park. (ungrammatical)

If xyz or not is not often used in conditionals, it can sound awkward, if not ungrammatical, and is best avoided if you you're a learner.

• #I'm going to the park if it rains or not. (awkward)

In conditional sentences, the word if is a preposition. It isn't a subordinator.

Interrogatives

If XYZ, if XYZ or not, whether XYZ, whether XYZ or not, and whether or not XYZ are all used in subordinate interrogative clauses:

• I don't know if she's working
• I don't know if she's working or not.
• I don't know whether she's working.
• I don't know whether she's working or not.
• I don't know whether or not she's working.

Notice that if or not XYZ is not grammatical:

• *I don't know if or not she's working. (ungrammatical)

The not versions in the grammatical sentences above don't seem to make much difference to the meaning. However, they make the negative versions of the embedded propositions more salient.

If the interrogative clause comes at the beginning of the sentence, in other words if it is the subject in the sentence, then we have to use whether and not if:

• Whether she's able to do this is unclear.
• If she's able to do this is unclear. (ungrammatical).

We also strongly prefer whether to if when the interrogative clause is the complement of a preposition, such as about:

• I'm unsure about whether she's there.
• I'm unsure about if she's there. (may be deemed ungrammatical).

Commas

Commas can be useful for differentiating condition clauses from interrogative ones:

• Let me know whether you're coming or not. (interrogative)
• Let me know, whether you're coming or not. (conditional)

The first question wants the listener to say that they are coming or aren't coming. The second sentence asks the listener to tell them something (we don't know what this is, perhaps it's who won the FA cup final). If the listener is coming we need an answer and if the listener isn't coming we still need an answer (about who won the FA cup).

Hope this is helpful!

Poorly-organized thoughts:

1. I disagree with your first 2b. "Whether or not you like this example is of no concern to me." seems valid to me.
2. I agree with Grammar Girl and Strunk & White: "make every word tell". "Or not" is typically useless.
3. In 1b, you assert that "whether" could not substitute for "if," but in your second 2b, the sentence is nearly identical and you do use "whether": "Call me" vs. "Let me know." I agree with you that "if" and "whether" have different meanings in these sentences, which I will explain below.
4. I agree with you that the sentence construction of 2c creates ambiguity.

The word "if" expresses a conditional situation. "Whether" only sometimes expresses conditions, however, because it is also used to express uncertainty: "I'm not sure whether I will go to the Britney Spears concert."

So, if we make an apples-to-apples comparison, we will limit the our use of "whether" to only conditional expressions.

Google has a lovely definition of "whether" for this sense, "indicating that a statement applies whichever of the alternatives mentioned is the case." Because the outcome is irrelevant, appending "or not" to "whether", when used in this sense, is always logically permissible, even if it is stylistically discouraged.

Presto, we have our answer. If the outcome of the possible alternatives it irrelevant, then "whether" is your word. If the alternative that actually occurs will have an effect, then "if" is king.

Edit, but see the comment below

Is "I'm not sure if I will go to the concert." incorrect? – EFrog