I was told it is very unusual to say 'I don't give a toss'. If so, why is that?
It is used colloquially in the UK, and possibly elsewhere, to mean 'I couldn't care less.' It is derived from the act of tossing a coin. If it is thought to be improper, it's probably because toss-off is a slang word for an act of masturbation.
I've never heard or read this expression, but it's easy enough to interpret. "Toss" is a euphemism for damn in this case. It differs in form and register but not in meaning. As an American speaker, I'd probably think it comes from "toss your cookies", slang for "to vomit". It may be unusual in American English. I don't know about British English or other varieties. If it's unusual, then it probably means that Snooki or Justin Bieber haven't used it on TV
I don't think that toss-off is American slang for masturbation, but the online slang dictionary says, as Barrie England confirms, that it's British slang for masturbation. (How many times does one get to use that word in a short discourse without raising eyebrows?)
Here's an interesting factoid. I don't know whether it's true, but it's fun to read: "The penalty for masturbation in Indonesia is decapitation." And then there's this: "Alabama Supreme Court Upholds Anti-Masturbation Law". I think I remember being told, when I was in the US Navy back in the mid-1960s, that masturbation was against the UCMJ (Uniform Code of Military Justice), but I don't remember looking it up. Any other veterans out there told anything like that in boot camp or barracks BS sessions?
Projectile vomiting (vomiting that ejects the gastric contents with great force) is arguably a type of ejaculation and, therefore, related to the desired outcome of masturbation.
In the British use of "don't give a toss," "toss" is a euphemism for masturbation, which indirectly infers the F-bomb. Americans don't draw a connection between "toss" or "tossing" and anything even remotely sexual, but typically will use the F-bomb in the same construction.
Before the arrival of BBC America (ca. 1998), most "British" dialogue that reached America was rather more proper, even highbrow. I mean, no one mentions "tossing off" in "Room With a View" or "Howard's End" or "The Man Who Would Be King." Or "Harry Potter." And the American public television channel (once the chief source of exposure to British English "conversations" for most Americans) always featured an equally sanitized British fare, such as "Rumpole of the Bailey" and "Are You Being Served?" They did air Monty Python's Flying Circus at one time (in fact, that was how the Pythons were introduced to the states), and the Pythons did drop the odd "tossing" or "sodding." But spoken in passing and with so little frame of reference, the non-British audience had to be paying especially close attention to grasp the meaning. Outside of public television, and before BBC America, the only British TV show I can think of that came across and was aired unaltered was Patrick McGoohan's wonderful "The Prisoner" series, and that was 1967-68. And there certainly wasn't any off-colour language in that, either.
And often as not, when American telly ...ahem ...borrows a popular British TV show (Sanford and Son, The Office, Shameless, Man About the House[=Three's Company], et Al), they re-cast it and re-script it and substitute "American" dialogue, so the Britishness largely gets filtered out. But when TV shows go the other way, USA to UK, there's more the tendency to keep the original content. So I think Brits tend to be more comfortable with American slang than the other way round.
So put "tossing" on the list of terms most Americans simply wouldn't get, along with "sodding" and "bugger." And without a frame of reference to draw from, most won't understand the significance of references to "a poof," "leg over," "chatting up," "randy," "rodger," "snog," or your "John Thomas," to name but a few.
As George Bernard Shaw said, "England and America are two countries separated by a common language."