The phrase au diable is idiomatic if it is followed by a mention of who/what you wish send to hell:

Au diable Trump !

Au diable les examens !

Au diable les journalistes !

Au diable le Brexit !

Au diable tout le gouvernement !

It is not idiomatic, however, to use it with tout alone (tout being a pronoun then). You can use rather use the longer form qu’il/elle/ils/elles aillent au diable with tous if you refer to multiple persons or items:

Qu’ils aillent tous au diable !

If by "to hell with everything", you want to express the idea that you are unhappy with everything and wish to "call it quits", you can use other phrases:

Je laisse tout tomber.

J’envoie tout valser.

Je m’en fous de tout.

We would not use tout on its own here, to my mind the closest if you do not want to specify anything would be :

Au diable tout cela !

“Au diable tout” is not a possibility in French; “tout au diable” is better from no more than a syntaxic point au view (as user Marroon says in a comment) but wouldn’t be found anywhere else than a special context: it can never appear in a translation of “to hell with everything” in today’s spoken French, the reference to hell is not used in this context except in the literature or in the language of certain people (I heard it last from a doctor’s mouth 15 years ago (Au diable l’avarice !)). Moreover, the most general possibility of a context in which all is considered to be rejected does not seem to exist in French.

I

(TLFi, diable¹) [En parlant de qqc. ou de qqn qu’on souhaiterait voir disparaître] Envoyer au diable, ou, sous la forme exclam. va, allez au diable!, par ellipse : au diable! Va au diable avec tes histoires! Au diable tout cela! Le cœur se rouille. Dérouillons-le. Et pour cela envoyons au diable les rancunes (BERNANOS, Lettres inéd., 1906, p. 1737). Oh! qu’il aille au diable avec son mulet! C’en est trop (CLAUDEL, Raviss. Scapin, 1952, préf., p. 1331). (user LPH‘s bold type)

Then, the literal translation exists in the old language and in the literature. However, it applies more specifically to a given set of aspects or things determined by the context ; a translation for the most general context will be considered after (II).

• Au diable tout cela !

In today’s French, as said above, this form will be rather rare. In formal language you can say something like this ;

• Assez de tout ça !
• J’en ai assez de tout ça !
• J’en ai par dessus la tête de tout ça ! On en a par dessus la tête de tout ça !
• Fini, tout ça !
• Fini, toutes ces complications !

In the colloquial language those forms are common ;

• Il y en marre de tout ça ! (Y’en a marre de tout ça !) _ J’en ai marre de tout ça !

Unfortunately, all those translations correspond rather to “I’m fed up with all that”; the specific refreence to the wish of an elimination of what people are fed up with is not specifically a possibility, unless you use the language that is beginning to be obsolete (Au diable …).

II

The following form is termed “populaire, familier” in the TLFi (popular language, colloquial); it can be used in “I” for a limited context but is used in extreme cases by people that wish to reject a whole existence (family ties, work, social ethos) as they have in mind to start a new life.

• He said “To hell with everything!”.
  Il a dit « Je plaque tout ! »

I’d say something along the lines of

“Oh et puis merde !”

That’s the first thing that would occur to me. To me, it’s the most idiomatic way of saying “To hell with everything”.

Truth is, I never ever hear people say “Au diable blablabla”…

In case you want to add more drama to your speech and be more vulgar, you might even say :

Qu’il(s) aille(nt) se faire foutre avec…

I strongly urge you not to use the latter, but those are the most idiomatic translations.

In Québécois, it is common, yet slightly vulgar, to say “D’la marde!” (literally “shit”).

One commonly used expression for “to hell with everything” that doesn’t have any religious connotation, isn’t vulgar, sounds less extreme (since French speakers tend to use a more moderate language than Americans on average):

Tant pis!

One would typically accompany this expression with a Gallic shrug.

Maybe the most polite forms might be “envoyer [somebody/something] au diable” or “tout envoyer au diable”, for example “j’envoie tout au diable” —— with the meaning “je laisse tout tomber”.

As far as I know, “envoyer au diable” is a bit archaic, “laisser tomber” is more modern, and both are colloquial :^)