Since Pesetsky (1987), wh-phrases with the hell, as in (1), have been extensively studied in the generative literature:
(1) Who the hell is she talking to?
None of this literature, to my knowledge (other than a footnote in Huang and Ochi 2004), ever mentions other uses of the hell. The purpose of this post is to set out some of the data. The syntactic distribution of the hell turns out to be quite limited.
There seem to be two non-question uses of the hell. The first is exemplified by the following:
(2) The hell you say!
(3) The hell I will! (responding to other person's request/command)
(4) The hell she did! (responding to other person's report)
In this use, the hell seems to attach to the left of a finite clause, and vehemently denies the validity of the proposition expressed by the clause. This use seems to be restricted to matrix clauses:
(5) *She said that the hell she will. (OK as quote: She said, ``The hell I will!'')
Note that the subject of the clause can be any person---first, second, third---, as exemplified by (2) through (4). (Plural is also possible: The hell we will! The hell they did!)
The second use has the hell to the left of a directional prepositional phrase (or particle):
(6) Get the hell out of here!
(7) I got the hell out of there.
(8) Get the hell into bed!
(9) The fox ran the hell out of the room.
(10) I drove my car the hell away from there.
Phrases other than PPs are not allowed:
(11) *I fled the hell the scene.
(12) *I got the hell lost.
(13) *I ran the hell as fast as I could.
(14) *I hope the hell (that) she's not there. (not to be confused with I hope to hell that...)
(15) *I wonder the hell where she went.
The hell cannot come before the verb, interspersed with auxiliaries:
(16) I was running the hell away when...
(17) *I was the hell running away when...
(18) *I the hell was running away when...
Although the hell seems to be attached to the prepositional phrase, it does not move as a unit with it. It cannot front with the PP in locative inversion, for instance:
(19) Out of the room ran the fox.
(20) *The hell out of the room ran the fox.
(It also can't be stranded: *Out of the room ran the fox the hell.)
It also can't front in a wh-question or relative clause, although stranding the preposition is fine:
(21) This is the person that he ran the hell away from.
(22) *This is the person the hell away from whom he ran.
Rightward shift seems to be possible:
(23) ?I drove my car on Thursday the hell away from there.
At this point I have no theory to offer of this peculiar distribution. (Few other phrases attach only to PPs; one is right, and that can move with the PP: Right out of the room ran the fox.) It is also unclear whether these three uses of the hell have anything in common, other than some kind of expressive content.
Huang, C.-T. James and Masao Ochi (2004). Syntax of the Hell: Two Types of Dependencies. Proceedings of NELS 34, ed. K. Moulton and M. Wolf, 279–294. Amherst, MA: GLSA Publications.
Pesetsky, David (1987). Wh-in-Situ: Movement and Unselective Binding. In Eric Reuland and Alice ter Meulen (eds.), The Representation of (In)definiteness. Cambridge, MA: MIT Press, 98–129.