Q:

How does the addition of のか to the end of a sentence affect the meaning?

I've always had trouble understanding か (question particle) in casual speech.  I read that in casual situations, か can be used to give the sentence an exasperated or sarcastic tone. Like in:
負けっかよ！　As if I'd lose!
I think that I understand that usage reasonably well.  What confuses me however is when か is used with a sentence that clearly should be a question (i.e. it has a question mark or a question word). For example:
やってみるか？　Want to give it a try?
I believe I've read that か is unnecessary (and not used) in casual speech to ask a question and questions are simply conveyed through a rising intonation or the addition of の（だ）.  Could someone explain how is the above sentence different in terms of tone or nuance from the same sentence omitting か 「やってみる？」?
Furthermore, on a similar note I believe, the sentence final particle combination のか？！ seems to occur frequently.  I'm not really sure what to make of this one.  I thought の　might be the explanatory の but how can one both explain and ask a question?  For example:
そんな嘘にオレがだまされっと思ってんのか！？  Do you think I'd be taken in by a lie like that?! (I'm not confident of this translation)
How would that sentence's meaning be affected if it were instead:
そんな嘘にオレがだまされっと思ってんの！？ or
そんな嘘にオレがだまされっと思ってんか！？
Thank you very much for reading my post to the end : ). I know this question isn't that specific but any and all help is appreciated.  Thanks again!

A:

Your translation was correct in meaning.

そんな嘘にオレがだまされっと思ってんのか！？

I think the latter is the more colloquial version of the following:

そんな嘘にオレがだまされっと思ってんですか！？(or思ってるんですか)

So this:

そんな嘘にオレがだまされっと思ってんの！？

has the same meaning with perhaps less inquisitive emphasis, while this:

そんな嘘にオレがだまされっと思ってんか！？

sounds less natural to me. I think one could say the sentence in the last way, but it becomes very slangy, almost to a rarefied extent. (perhaps it would sound immature or "country" to a native listener, but I lack the expertise to say)
So in conclusion, yes, you can make a sentence a question simply by altering the tone of the words, but obviously adding か makes it a more "complete expression."
ex.:

これ食べる？ You eat this?
これを食べますか？ Do you eat this?

