Learn English – How offensive is calling someone “dodgy”

Before getting to the main answer, a few points that may be interesting to you (though I realise they're not actually part of your question!):

1. In the UK - at least in some circles, the word cunt is an insulting word for a man, never a woman: neither I nor those that I've asked have ever heard it used that way, though as the comments below attest, this usage does exist.
2. Of the others, the odd-one-out to me would seem to be bitch: I'm not sure about US usage of that word, but to me the others all have a connotation (to a greater or lesser extent) of sexual impropriety. In the UK at least, bitch doesn't have that association - it means something along the lines of woman with an unkind, evil or spiteful personality.
3. The words skank and ho are recognised - especially from rap music - but are definitely felt to be American imports. All of the others are fully accepted as native :)

On to the main question: it's probably worth distinguishing between the degrees of offensiveness of (abusing terminology slightly) use and mention of the words: that is, some words can be happily used in polite society, but one would be highly offended to be called one - whereas with some words merely saying the word (regardless of who it is applied to) is offensive in of itself.

Having drawn that distinction: mention of the word slag - while it's clearly to be avoided when on one's best behaviour - is unlikely to cause much offence; that would put it on a roughly similar level to slut or perhaps skank.

However, using the word slag to describe someone would be a good way to start a fight. It is probably at a similar level to slut: perhaps slightly more offensive, if only because slutty/sluttish can refer to general demeanour (in dress, speech) - and indeed can occasionally merely mean "untidy, slovenly" with no sexual connotation - whereas slag is unambiguously referring to sexual behaviour.

It's worth mentioning the word is used a lot in comedy - perhaps the earliest was in the comic Viz (decidedly not a comic for children, and never noted for its reverence); here's an example in Harry Enfield's sketch show; and more recently in Gavin and Stacey. (Using the word for men isn't common except in reference to this show!). You can probably see - especially from this last example - that this word can be thrown around among close friends in a humorous way - but I would strongly advise against doing so unless you're very sure of what you're doing, since the line between banter and offence is a very narrow one at times :)

I've never heard that used as a derogatory term. But then I've never moved in circles rich enough to hire gardeners. The conventional derogatory term for Mexicans in America is "wetback". But if some are now using this term as an insult, I guess you have to be careful with it.

If a Mexican is a skilled brain surgeon and you called him a "leaf blower", I guess he'd take that as an insult. But if two Mexicans were working on the lawn and you said, "Jorge is the weed puller and Pedro is the leaf blower", that doesn't sound insulting to me, but a simple statement of fact. If someone said he was offended by that, I'd just reword it. Like say, "Jorge is pulling the weeds and Pedro is cleaning up the leaves" or some such.

If someone routinely refers to all Mexicans as "leaf blowers" ... well, it sounds like an odd insult to me, but he presumably intends it as an insult. People can be super-sensitive about words, but if someone is clearly TRYING to insult you, I think you have a right to be offended.