Yesterday I saw a lesson of English on TV. The teacher asked to some people to translate (from Italian) some expression. One is: "What can you say to a person to invite him into your office?" and lot of people answer: "Can you come in my office?". The teacher said that it is wrong, because it sound like an erotic invite and the correct sentence is "Can you come to/into my office?" Is it correct? Because here: What do I have to say when I enter into a house? someone answer me to say "May I come in?". Is it misleading?
"Come in" is the right translation of entrare.
But with a location it would normally suggest movement from one place to another. English doesn't really use cases to communicate this, so we use prepositions like into and out of to indicate movement. Therefore "come into my office" would be correct.
"Come in my office" suggests an action which takes place entirely inside the office - the sense of entering is lost - so it's easy for someone with a vulgar mind to think of the ... sexual meaning of the verb "come". The true meaning would still be understood, but saying/writing it this way might produce sniggering from teenage boys.
"Can you come in my office" does not sound like an erotic invitation. The problem with that sentence is that "come" is being used as a verb of motion with respect to "my office", so you need a preposition that refers to motion, rather than "in" which refers to being static.
"May I come in?" is different because although the action is literally the same, there is no (stated) object to pass "into" - instead once one has "come", one will be "in". (And for the foreign reader, that last sentence does sound like cheap innuendo).
"Come into" and "come to" are better than "come in" because they convey transition (from outside to inside). As njd said, "come in" is inviting snickering from teen boys.
The other aspect of your question is "can" versus "may". "Can" is about ability while "may" is about permission, so "can you come" (are you able to come) and "may I come" (do I have permission to come) are the right forms there. When asking someone else to meet/join you, you may also see "will you" (are you agreeable to this).
I suggest avoiding "can I come in?", which will prompt the smart-alecks to say "I don't know, can you?" -- that is, are you capable of doing so?