Get hold of, get ahold of, get a hold of

“Get ahold of” doesn’t exist. “Get hold of” and “Get a hold of” are mostly interchangeable, but “get hold of” is more often used with people: “get hold of Mr. Jones and tell him…”, and “get a hold of” is used with things, like gaining expertise: “I think I’ve finally gotten a hold of this subject…”.

Edit: New information: “ahold” does exist, but it’s a slang. Thanks, @NewAlexandria.

"get a hold of" is the only proper form. I would prefer this in all circumstances since it is correct use of the language.

"Ahold" is not a proper word.

"ahold of" is a colloquialism, but the OED does not define "ahold" as a word out of context of the colloquialism.

"get hold of" is just a broken form, where the speaker couldn't manage to use the article "a".

I suppose I would use the incorrect forms in social contexts where being seen as a 'non-native speaker' would put me danger (perhaps if I was confronted by gang members)

I think that grammatically speaking, get a hold of yourself doesn't make much sense - and in fact it seems to me that people originally recognised this.

That linked NGram chart shows how the more "logical" get a hold on yourself was actually more common when both expressions started becoming widespread in the 20s. And this one shows that plain get hold of yourself has always been more common than either version with the word "a".

Whilst I don't disagree with other answers saying that "get ahold of yourself" is "incorrect", that link to over 15000 written instances shows that in the minds of many, it really is a kind of "adverb" that gets round the inherent grammatical problem in what's now an established idiomatic usage. Somewhat akin to, for example "Get along with you!" (meaning "Go away!", "Be off with you!").

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EDIT: Per comments below, I would just note this one semantic distinction...

1: "I'm trying to get hold of John" (to locate, contact, communicate with him)
2: "I'm trying to get a hold on John" (to physically grasp him, or metaphorically understand him)

There's a certain amount of flexibility in the above constructions (dialectally, at least, #1 could use ahold, and it could carry the sense of #2). But the #1 make contact sense always needs of, and if you try replacing hold with grip, grab - with or without preceding get [a] - it should be clear that idiomatically, certain forms either don't work at all, or have restricted (probable) meanings.

First off, any time you have 'get' followed by some noun form of an action verb, it's going to have the sense

• to succeed in ~ing, to have an opportunity to ~

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so, in this instance,

Get hold of

1. to succeed in grasping, to happen to get a hold upon.

   Matthew Kellison, A Survey of the New Religion, 1603, p. 664:

   For if a man by ſhipvvracke vvere in daunger of drovving, then ſo longe as he ſeeth humaine meanes to ſaue him, he vvill ſnatch at a cord vvhich is caſt vnto him, or he vvill reach for a borde, or ſeeke to get hold of a boate, rocke, or tree, to helpe him ſelfe by; & if he be an Atheiſt, then ſo longe as theſe meanes faile not, he ſeeketh for no other, but if he perceue, that by no creaturs helpe, he can be holpen, then be he Chriſtian or Pagane, Ievv or Atheiſt, he thinketh vppon ſome higher povver, and vvhen all creaturs forſake him, and his ovvn force vvill no more ſerue him, nature bidds him to ſeeke farther, & to demaund that helpe of the Creatour, vvhich no creature can yeeld him.

2. (figuratively, of objects) to succeed in gaining possession of, to get.

3. (figuratively, of concepts) to succeed in grasping intellectually, to gain an understanding of.

4. (figuratively, of other people) to succeed in reaching, to make contact with.

So, all in all, pretty useful and fills a need in the language for communicating both success and the longing and effort that preceded it.

Some dictionaries (e.g., MW) consider this the most proper form and it's certainly seen more usage than the others. All the same, as an American, I'd only instinctively use it for the first sense and process—and use—the three figurative senses as clipped forms of 'get ahold of'.

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Pace @NewAlexandria & co., there's nothing substandard or confusing about

Get ahold of

1. [alt. form of] get hold of, emphasizing the specific strong action involved.

Graham's Magazine, Aug. 1850, p. 119:

The good sailor who had caught ahold of her when she was fallin', told her to cheer up.

It's a straightforward application of the English prefix 'a-' based on the old 'a' variant of 'on'. Specifically:

ahold, adv.

2. So as to hold on to someone or something; with a firm hold or grip. Chiefly with of.

Some dictionaries (e.g., Cambridge) affect that this is an Americanism, but the OED and MW note that it appears elsewhere in vernacular and regional British English as well. The truly colloquial American form is 'aholt'.

@Nora is right that the cretic rhythm of 'get ahold' is the main reason to prefer it to the spondee of 'get hold'. This discomfort means the speaker has to make a particular effort to say it this way and @JanusBahsJacquet correctly pointed out above that this makes 'get hold' sound more formal and stilted than it really should be. Moreover, the adverb also emphasizes the action being described and heightens its force, which makes it superior for any of the figurative senses of the phrase.

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Get a hold of

1. to get a cargo hold of.

2. [Misspelling of] get ahold of.

3. [Mistake for] get a hold on.

@NewAlexandria has this one backwards as well. It's 'get a hold of' that can be accepted as a common enough regional idiom but which makes no sense based on its component parts. It either uses a as a preposition meaning 'on' (which hasn't been standard since the 1700s outside of set phrases like 'once a year' or in dialects like Geordie) or treats it as the indefinite article, which doesn't work with its following preposition 'on' unless you're describing a 'hold's-worth' of something, which only works with as a clipping for 'cargo hold'.

Obviously, I'd never use this form myself but plenty do, probably mostly because they take it as the indefinite article, don't sweat the trailing preposition's mismatch, and don't realize that ahold is a perfectly valid word.