I'm wrong; MWDEU does say something about it, although it's nothing conclusive:

"It may seem that was is crowding out subjunctive were in informal contexts, such as the letters and journals among our examples here. But not necessarily:"

...and they go on to cite some examples to the contrary.

Well to be honest I'm not convinced that the difference is one of formality. MWDEU says nothing about a difference in formality. And the englishclub.com site simply asserts that this is so. In the writing of good writers we find both "was" and "were" forms, sometimes both in the same paragraph.

As I've already said, "informal" does not mean "incorrect".

I am interested in correct usage, but I find it more useful to take "correct" to mean "how good writers actually write", not "how someone thinks I should write". Good writers use "if I was" and "if I were" interchangeably. I have provided a link to Merriam-Webster's Dictionary of English Usage, which discusses the evidence in detail.

But other people have continued to assert that "if I was" is wrong, simply because they say so. I don't find assertions without evidence very convincing.

David Teague: The verb "gift" is not a backformation from "gifted". "Gift" was a verb in the 15th century meaning "to endow with some power or attribute" and this is where the past participle "gifted" came from.

In the 17th century, the verb came to mean "to present", and it continues in this meaning today.

Simply stating that it is nonstandard does not make it so. I have cited a reference (Merriam-Webster's Dictionary of English Usage). I recommend reading the entry: http://books.google.com/books?id=2yJusP0vrdgC&lpg=PP1&dq=merriam-websters%20dictionary%20of%20english%20usage&pg=PA477#v=onepage&q&f=false

MWDEU is a dictionary of standard English, from both NA and the UK. I suggest that you read the preface and introduction:
http://books.google.com/books?id=2yJusP0vrdgC&lpg=PA877&vq=subjunctive&dq=merriam%20websters%20dictionary%20of%20english%20usage&pg=PP10#v=onepage&q&f=false

Perfect Pendant
"Unfortunately Merriam-Webster tends to reflect only what is common or acceptable in North America"

This is not true. MWDEU quotes equally from NA and UK writers and usage commentators. If there is a difference between NA and UK usage, or between NA and UK usage commentary, they say so.

Brus
"English usage and correct (as you say, formal) English are not the same thing."

You seem to be equating "formal" with "correct". But "formal" doesn't mean "correct", it means "formal". And "informal" doesn't mean "incorrect".

Also, I don't see why you think that "was" for "were" comes from North America. Many of the examples given by Merriam-Webster's Dictionary of English Usage are from authors outside of North America: Carroll, Byron, Thackeray, Farquhar.

No, I was sincerely interested in what how you interpret the difference between "was" and "were", since for me, there is no difference. I have heard that for some people, "were" indicates a lower degree of likelihood than "was".

It seems that for you, "was" in a present counterfactual is unacceptable. If you see a sentence like
"If I was a cad, I would apologize."
you interpret it to mean that there is another clause coming. Left as it is, it doesn't work for you.

That's fair enough. However, the fact is that writers use "was" and "were" interchangeably in this context (according to Merriam-Webster's Dictionary of English Usage). Where there is a difference it seems to be one of register. That is, "were" is more formal.

Perfect Pedant
It seems to me that "if I was" can only lead to ambiguity if it is used in the same context as "if I were". If my two sentences really do have different meanings, then there is room for confusion, and I'd like to know exactly what the difference is.

Your sentence "If I was a hopeless cad, I apologize" refers to a past event, so it's not the same context as my examples.

Would you ever use "if I was" in exactly the same context as "if I were"? Would you say this:
"If I was a hopeless cad, I would apologize."

If I was the Prime Minister, I would change the law.
If I were the Prime Minister, I would change the law.

Don't both of these sentences refer to unreal present events? If I can't remember if I was Prime Minister, I would be talking about a past event. I might say:

If I had been the Prime Minister, I would have changed the law.
or
I can't remember if I was the Prime Minister.

The whole sentence determines whether the event is counterfactual, not just the verb.

For people who make a distinction between these two sentences, what exactly is the difference?
If I was the Prime Minister, I would change the law.
If I were the Prime Minister, I would change the law.