difference between "i am home", "i am in home", and "i am at home"

Difference between 'I am home' and 'I am at home'

• Yes, there is marginal difference. The preposition ‘at’ indicates that the noun ‘home’ that follows it, establishes a point in relation to which another object ‘I’ is positioned.
  So: “I am at home” always means that I am positioned or staying at home, and this is normally used.
  Where as the term “I am home” can be used to mean; I am safe after some incident. Look at the following sentences: 
  My friend had a surgery for removal of a tumor. I am happy to hear that he is home and doing well.

• Why do you think it's right to say "I am home"? It can be correct, for example, if you come home and your wife is in another room, you could call out "I'm home!" But if you are talking to someone on the telephone for instance, you should say I'm at home or I'm at the office.

• I think, "I am home" is an Americanism (slang)

• If I may add a suggestion, I'd say "I am at home" is neutral, you simply tell someone where you are, but you would usually not say this to someone who is already there; you say "I am home" when you have just arrived, and you would usually say this to someone who was already there.

• Most of the time these two expressions are interchangeable in common spoken American English, although there may be some difference in "correctness" that matters to experts--if there is, I don't know it.
  
  There is also the use of "at home" with a somewhat different meaning, of "comfortable" or "at ease". Example: "Is she at home on the golf course?" , meaning, is she used to being there and does she know what she's doing there. This is, of course, not the same as "estoy in casa", but you should be aware of it.
  
  There is also the expression "home free". Example "He is home free", meaning he has reached the goal he was seeking, and has not come to any harm or received any penalty to get there. This expression comes from a game.
  
  Expressions like "where's he at?", however, are not considered acceptable in standard English, although they are very common (and I do not personally object to them). It is interesting that such an expression is not permitted, because the answer might very well be "he's at home"! But language is not always sensible.

• From an English point of view, in the context you gave in a later thread, I would say that "I'm at home" is the more usual reply.
  
  I would only use "I'm home" when you actually arrive home, walk through the front door and shout "I'm home" to other people in the house whom you cannot see. 

I am in home/i am at home? 

• It would be either: 
  
  "I am in my home." or "I am at home."

• neither is correct until you add my , his ,etc after at or in 
  
  i am at his home , i am at my home

• "I am in my home" is correct. If you are in any public place then 
  " I am at the mall" or " I am at the park"

• two sentens are correct. i am in home means i am in home.but i am at home means expert in any work

“I'm home” or “I'm at home”

• The second form looks more correct to me, but the first expression is present in several titles of movies and songs. Which form is preferable?

• I think the implication in the expression "I'm home" is that you're home from somewhere. It may, as Mitch says, be that you've just come/gone in, but it doesn't need to be — you can be home from the front or home from university and have been back for a week or so. But a homecoming in the not-too-distant past is certainly connoted.
  The nature of the word home in "come/go home" is often argued over; noun and adverb are suggestions, but directional particle is what I'm voting for at the moment. Apparently, home in go home can be used without a preposition because it is the remnant of an earlier form that fused preposition (to) and noun, and when this type of inflection for case disappeared from English, this particular usage continued, with the to-home form standardising with the base noun. We don't have "I'm going school". Possibly, "He is home" has arrived via "He has/is come to-home". Homein "He is home" is locative rather than directional now.
  It may be another legacy from the fused to-home that we never use the preposition to with home(except with an intervening determiner etc.), but this is true for other nouns also.
  Certainly, other prepositions (at, from) can be used with the noun home in the expected way, and "I'm at home" is strictly locative. To express arrivals at other venues, we are forced to use a different expression — "I've just got to school / I've arrived at school", as psmears says.