Difference between なんか、なんて、など

なんて and なんと／など are completely separate from なんか.
なんて is the formal way of expressing yourself. It's almost like a prefix in English (except for the part that it's not thrown in front of a word, but instead it's just put in front of a sentence).
So you could say:
きれいな 女の人 だろうね
That's a beautiful girl.
If you throw in なんて, you only stress the meaning of what you are saying.
So
なんてきれいな女の人だろうね
What a beautiful girl she is!
The meaning is the same; all you've done is stress what you're saying.

That said, you can also throw なんて in the middle of a sentence.
トムがおばけのことなんてしんじられない
Tom doesn't believe in ghosts.
I'd like to note that you are being emphatic when you say this though. Much more so than had you left なんてout.

If なんて is at the beginning of the sentence, you can use なんと instead.
If it comes in the middle of the sentence, you can replace it with など. Simple as that.
Just note, that なんと and など are more familiar, so should only be used in casual situations.

なんか: That is the word that is similar to  "like". That's the word you throw in when you're trying to think of what you're going to say.
Example:
なんか、どうしよう？どこ行くだろう？あのさあ、なんか、この町のおいしいところはどこだろう？
Like, what should I do? Where should I go? Excuse me, but umm... where can I go for some good food around here?"
なんか is basically used for "like" or "umm" as we would English, and I don't think I need to explain to you that it's very informal.


Source: http://answers.yahoo.com/question/index?qid=20100424195808AAGfq7F