Exposure therapy is the usual treatment.
If "he" sounds right, use "who"; if "him" sounds right, it's "whom".
Or rather, only use it if you intend to go the whole hog and comply with all the pedantic, pseudo-latinate prescriptions of traditional formal English grammar.
"It is I."
"Bad grammar is something up with which I shall not put."
"This is an historic occasion."
And so on....
What's wrong with this? I cannot think of another way in which to say this?
It's a long story. If you've never had to deal with this quaint piece of British pedantry, count yourself lucky. But you can still sometimes here BBC journalists who say "This is an historic occasion." with both the "n" and the "h" pronounced clearly.
The who/whom I/me distinction isn't a pseudo-Latinate grammatical prescription - it's the last vestages of overt case marking in English. An + words starting with "h" is a phonological side-effect of h-dropping in some dialects.
The preposition stranding thing, though, is pseudo-Latinate prescriptivism. That and the supposed wrongness of split infinitives are my two biggest annoyances with "proper" grammar.
Some are prescriptivist rules for how grammar ought to be, some are observed facts about how language functions.
On that note, it reminds me of a company I did some work for recently. They never used "me", only "myself": "Yes, he gave it to myself on Tuesday."
I doubt anyone would argue that "myself" is archaic, but people using it incorrectly is definitely jarring.
Probably better advice. There's a bit of research literature on the death of "whom". I can't remember when exactly, but I want to say around the beginning of the 20th century it pretty much died out from the language. It's a nice progression, English doesn't use thee, thine, thy or thou anymore either.
re:myself.
That's just plain weird.
- the OED remarks "whom is 'no longer current in natural colloquial speech'" and notes multiple cases in Shakespeare, Defoe, Chaucer and the King James Bible where "whom" is used "incorrectly" by modern standards
- Howard Lasnik and Nicholas Sobin describe whom as "It is commonly assumed that the English interrogative/relative pronoun whom is parallel to him and them in manifesting objective pronominal Case...Whom in modern English derives from a set of extra-grammatical rules...[used to generate] products that have a 'prestige' status. Whom differs markedly from intuitions about the use of personal pronouns. http://ling.umd.edu/~lasnik/ and the presentation http://academics.utep.edu/Portals/878/papers/whom_paper_vanc...
- Edward Sapir dedicated significant studies to the obsoletion of whom. In "Language: Intro to Study Speech" he remarks: "It is safe to prophesy that within a couple of hundred years from to-day not even the most learned jurist will be saying "Whom did you see!" By that time the 'whom' will be as delightfully archaic as the Elizabethan 'his' for 'its.' No logical or historical argument will avail to save this hapless 'whom'"
- Thurber provided this example: "A common rule for determining whether 'who' or 'whom' is right is to substitute 'she' for 'who', and 'her' for 'whom', and see which sounds better. Take the sentence, 'He met a woman who they said was an actress'. Now if 'who' is correct then 'she' can be used in its place...'He met a woman she they said was an actress'.
- Chomsky wrote that similar non-grammatical structures that only exist in grammar books are: "...a violation of natural law. In fact, a good deal of what's taught is taught because it's wrong. You don't have to teach people their native language because it grows in their minds, but if you want people to say, "He and I were here" and not "Him and me were here," then you have to teach them because it's probably wrong.
- Mair notes that: "whom is moribund as an element of the core grammar of English, but is very much alive as a style marker whose correct use is acquired in the educational system [, where it is taught]. [The use of whom] is highly restricted, but rather than disappear entirely, the form is likely to remain in use for some time to come because of its over prestige in writing."
I love how serious inquiry into language almost always reveals that the "Rules" are wrong.
Fixed that for you.