Is it incorrect to say, 'Give me it' ? I am told that it is and one should always say, 'Give it me'?
"Give me it" sounds very odd in Standard English, but so does "give it me". If you want to be on the safe side, I would go with "give it to me".
There are, however, dialects where "give me it" and "give it me" are acceptable or even preferred, see e.g. this BBC article:
Lancashire is a rich area in which to study accent, dialect and grammar as Willem [Hollman, an expert in linguistics and a lecturer at Lancaster University,] explains: "If I were say, playing with my pen in a very annoying way, and you were to take the pen away from me, I might tell you, "Hey, that's my pen, give it me!" but there's also speakers who wouldn't say "Give it to me!" but who would say "Give me it!" and then there's also speakers who would say "Give it me!" This last order "Give it me!" is not very common in Britain in general, but what we find in Lancashire is it's actually the preferred pattern."
I also found this interesting quote on Google Books, in a book titled "The Edinburgh history of the Scots language":
[...] there is some indication as to what might have been happening to the serialisation of indirect and direct objects in the course of the Modern Scots period in Cheshire et al. (1993: 74). They point out that, in English, "give me it is a more recent construction than give it me, which in turn is a more recent construction than give it to me, where the prepositional group to me reflects the function of the Old English dative case". They report that Hughes and Trudgill (1987) give the order give me it as that most usually cited in descriptions of present-day standard English, but they also state that the reverse order is common among educated speakers in the north of England and is acceptable to many southern English speakers as well. This would suggest that [...] the order [...] give me it is gradually taking over from give it me and the even older give it to me. No dates are given here for the introduction of the newer word order in England, but it would appear that Beattie and his fellows objected to give me it because it was an innovation rather than, or as well as, because it was a Scotticism.
The construction is perfectly good: in English, you can put an indirect object before the direct object, without a preposition, as
Give the dog a bone.
Give the man a cigar.
However, I find it a bit awkward to do so when the direct object (the thing you are giving) is a small as the word "it", and would more likely say give it to me.
On the other hand, I find no problem with show me it.
The it should refer to something that is already known, as used to avoid repeating yourself. Instead of:
That's my book. Give me the book!
you could use:
That's my book. Give me it!
You would hardly say "Give the book me", even if the special form "Give it me" is used in some places.
If both me and it could be understood by the situation, you could just say (but perhaps not write):
That's my book. Give!
Give it me (Gib es mir) and Give it here (Gib es her) both sound like an Americanized version of how the (correct, I should add) German version is uttered. I am a linguist also, and I would not be surprised if the origin of these two utterance was indeed German (not Germanic, I mean German, literally), spoken somewhere in the northern region of the east coast, most likely Pennsylvania.
It is common to encounter lots of sentences like these in areas such as Pennsylvania, where there has traditionally been a high number of settlers from Germany. This is also where you would hear sentences such as "Can I come with?", which is a word-by-word-literal translation of the German version "Kann ich mitkommen?". Many of these have been taken over by literal translation into English by settlers, and taken over into English grammar in that area, whereas one would not hear people say that further inland.
I don't know if this thread is still live but I have encountered "give it me" in literature up until about the second world war in southern English, even though I would say it is almost exclusively a northern construction today. I think perhaps it is an archaic construction, common in early modern Shakespeare, which carried through to what Mitford identifies as "U" (as opposed to "non-U") English, similar to expressions such as "wait at table" which omits the "the" before table. "Give it me" occurs in E. F. Benson, for example, whose prose so carefully reconstructed the language of the upper middle class of the inter-war years. Similarly I am sure it appears in E. M. Delafield's works. "Give it to me" is certainly more natural and is more correct now that the old usage has fallen away, though I fancy in its day the other would have been favoured by linguistic pedants.
Interesting direct American German theory, reminds me of standpoint/ Standpunkt whereas in the UK "point of view" seems to be more common. However, it's also possible as an Anglo-Saxon heritage that dates right back to the first millennium settlers in England. Many traditional dialects in England sound very similar to modern Dutch, which obviously is also very similar to modern High German.
I've certainly heard both "give it me" and "give me it" in working class England.