Is the question "Did I say I would take the job even if it was offered?" logically correct?

It's fine.

Here's what (I think) you meant:

"I did not say I would take the job, even if it were offered."

That's also logically fine. None of the clauses contradict each other. Generally, you cannot take a job until you've been offered it, so "even if it were offered" adds the useful information that your decision to take the job or not doesn't matter at this point in time.

You have correctly noticed the "negation" of the words you actually said ("Did I say" -> "I did not say"), but you came up with the wrong reason for it - largely because there isn't really a reason for it at all! The only reason why this question means the opposite of its words is because we English speakers have decided it does.

Rhetorical "say" questions

Questions of the form "Did I say X?" are often rhetorical.

Did I say I was there? - I was not there.
Didn't I tell you we'd win? -I told you we would win.

I should note that often it's only the tone of voice used by the speaker that makes this kind of question rhetorical: if you re-read Number 1 in a puzzled tone of voice, it becomes a normal question again.

This negation is not due to grammar - it's a technique of rhetoric: Make your point by first stating its opposite, then rejecting that opposite: "Did I flee from Rome? No, I did not!" In casual speech, the "rejection" part is usually left out, leaving just the rhetorical question alone, but we're so used to hearing it, we can mentally fill in the rest.

The pattern is simple:

Did I say I was there? = No, I did not say I was there!
Did I say I would take the job, even if it were offered? = No, I did not say I would take the job, even if it were offered!

So, knowing that your original question is rhetorical, it can be converted into a more direct assertion using the same rule:

Rhetorical question: Did I say I would take the job, even if it were offered?
Assertion: I did not say I would take the job, even if it were offered

Sub-clauses

Your next pitfall was in identifying what part of the sentence is acting on what other parts.

"Even if it were offered" and "I would take the job" are sub-clauses. The main clause of the sentence is "I did not say".

Because the main clause is "I did not say", it is this clause, and not "I would take the job", which is intensified by "Even if...". It's also not a redundant clause: no other part of the sentence states that you haven't received an offer.

P.S. Commas are important

There are two readings of your sentence, depending on where the comma sits:

"I did not say {I would take the job}, {even if it were offered}."
"I did not say {I would take the job {even if it were offered}}."

Here, we're lucky because only Number 1 makes sense. (Number 2 is illogical because the job being offered is a prerequisite for you taking it. It would be like saying "I would eat that cake even if I was able to eat cake"). In other cases, the reading can be more ambigious, and that's where the commas come in.

P.P.S. "were", not "was"

Strictly speaking, the original question is grammatically incorrect. Your "if" is an example of what's called the Second conditional form. The clause "the job [to be] offered" is referring to an action which may or may not occur, so the correct form of the verb here is "were", not "was". It's "even if the job were offered". This mistake is very common in speech, and is almost acceptable in some spoken English dialects, but not in written English.