I know the meaning of "have been had" is "been cheated". What is the origin of this idiom? It is really special in the sense that none of the individual words in this idiom convey the meaning of deceit in any way.
Reference.com puts this at early 1800 slang. In addition to "cheated," it can also mean "used" or "deceived." It could, then, mean "had [his or her] way with." So to say "I've been had," means "someone had his way with me." to indicate that you were used, cheated, or deceived.
Here are three takes on the origin of "have been had" in the sense of "have been cheated."
Eric Partridge, A Dictionary of Slang and Unconventional English (Fifth Edition, 1961):
have v. To cheat (—1805) : perhaps originally cant [that is "language of the underworld," in Partridge's terms]. G Harrington, in The New London Spy, "Had, a cant word ... instead of ... cheated." —2. Hence, to trick, deceive (1821) : low slang. —3. Hence, to humbug, fool (—1893; probably as early as 1825), low to general slang.
Robert Chapman and Barbara Kipfer, Dictionary of American Slang (Third Edition, 1995):
be had (or taken or took) 1. v phr by 1594 To become a partner in the sex act. 2. v phr by 1805 To be duped or cheated; be vicitimized.
Christine Ammer, American Heritage Dictionary of Idioms (1997):
be had 1. Be outwitted; also be cheated, deceived. This expression employs the verb to have in the sense of getting someone in one's power or at a disadvantage. [Slang; early 1800s] 2. Be bribed or influenced by dishonest means. [Slang; early 1800s]
These sources don't entirely agree about how "have been had" came to mean "cheated." Partridge suggests that it originated as an underworld euphemism, in which case the motivation is the same as for calling a robbery a "job": to avoid incrimination if overheard. Chapman and Kipfer point to a much earlier usage involving sexual intercourse, where "to be had" plays much the same euphemistic role as "to know." And Ammer seems to take the view that the usage originated in a simple extension of "have" in the sense of "possess," first to the sense of "have in one's power" and thence to the sense of "exploit one's advantage over."