There is no difference in meaning between these three sentences, unless the speaker already establishes a context.
He's a bit angry
This means he is somewhat angry.
He's a little bit angry
This means he is somewhat angry. No native speakers would infer any qualitative difference in how angry he is, unless someone first said
John: He's a bit angry (meaning fairly angry)
Mary: No, he's only a little bit angry (meaning not as angry as John implied)
When used alone, "little", "bit", and "little bit" all mean "small". But if you emphasize "little bit" over "little" or "bit" then you are emphasizing how small it is.
If I walked up to you on Monday and said "I'm a bit hungry", and on Tuesday I walked up to you and said "I'm a little bit hungry", there is no way decide that I'm not as hungry Tuesday as I was Monday. But if on Wednesday I said "I'm a bit hungry", and you said "Have a hamburger", I could clarify that I'm not as hungry as you think, by saying "I'm only a little bit hungry".
The theory of adverbs (and of Conjunction Reduction) given by McCawley in The Syntactic Phenomena of English explains why you can't get your example
*"I'll go tomorrow and quietly."
It would have to come by Conjunction Reduction from
[[I'll go] tomorrow] and I'll [[go] quietly]
but Conjunction Reduction requires the two constituents to be conjoined to occupy the same place in the original conjoined structures. That is not the case here, as I've indicated with the brackets -- "tomorrow" is a sentence modifier, but the manner adverb "quietly" is a V' modifier.
Best Answer
Tennyson writes
So your first sentence is not an unheard of construction.
This gives the suggestion that he provides help infrequently. It also sounds formal and literary.
This sentence sounds like he's trying to make his friends smaller.
This sentence could mean infrequently; it also sounds like he's just generally not of much help. It is less formal-sounding too.
This last one, I think we've all agreed, is probably the most common way of expressing what you are trying to say, although gmcgath is right in the comments, where he says that
is more usual.