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Theatergoers generally expect actors to abide by certain longstanding conventions, and if actors fail to oblige, it usually isn’t intentional. We assume, for starters, that people portraying other people are going to speak so we don’t have to strain to understand them. Emotions, even mixed emotions, should be rendered with comparable accessibility and with a flow that passes for a smoother, larger version of the real thing.

We should never, ever be aware of the gap between actors and their roles, a state that suggests that the performers are either miscast or inadequate, nor of the effort or strain that goes into creating the illusions of other lives. (Theater is not an athletic event.) And heaven forbid that any performer should directly or indirectly question our responses to a performance as it is occurring.

Well, that’s the way it is on the mainstream stages of Broadway, anyway. But had you stepped into the well-packed margins occupied by more adventurous theater artists in New York in recent weeks, you would have heard the crashing, tearing sounds of every one of these rules being willfully shattered and shredded.

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Consider, for example, the close-attention-demanding ensemble that animated the Australian-born “Ganesh Versus the Third Reich,” in which most of the cast members had “intellectual disabilities.” Or the Israeli troupe of blind-and-deaf performers in “Not by Bread Alone.” Or the actors who chose to act badly in “Inflatable Frankenstein” and “Seagull (Thinking of you).” Or even the British chap who showed up — in a children’s theater production, no less — to confront young audience members about why they were laughing at his character, a tattered refugee from Shakespeare, in “I, Malvolio.”

Of these “Ganesh Versus the Third Reich” (part of the Public Theater’s Under the Radar festival) is the most daring and probably the most illuminating. Created by Back to Back, a 25-year-old Australian company devoted to work featuring disabled actors and staged by Bruce Gladwin, “Ganesh” offers no prefatory explanations or context. It begins with three men discussing a drama about to begin rehearsals.

That play, one of them explains, is “a story about power.” Actors will be required to be Nazis and Jews and ancient Indian gods, one of whom, Ganesh, visits Germany in the age of Hitler. It takes you a while to register that the effortful speech and movements of the men having this discussion are not just actors’ interesting choices. These guys are this way naturally.

As the show continues — moving between the fantasy play and the back story of those behind it — it emerges that acting in it is a struggle for the performers in more ways than one. They argue about what right they have to embody persecuted Jews or their oppressors. Fights flare up, and the rehearsals too become a study in the uses and abuses of power.

The unctuous director, a conventionally handsome and well-spoken man, isn’t above playing head games with his cast members, particularly the recalcitrant ones. At one point he imagines a confrontational moment with an audience in which he taunts it for coming to “see a freak show.” He also appears in that show as Dr. Mengele, speaking about his fascination with “degenerative” human types.

A sort of revolution of the oppressed occurs in both narratives of “Ganesh.” But every time you think you’ve sorted the show into tidy parallel lines, it deviates onto another quivering tangent. Neither of its stories so much ends as trails into a disturbing ellipsis of unresolved questions. The last image, centered on the most conspicuously speech-impaired actor, is less one of triumph than of confinement, a sense of someone imprisoned by prejudgments that refuse to disappear.

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“Not by Bread Alone,” which runs through Feb. 3 at the Skirball Center at New York University, is more straightforward and even old-fashioned in presenting disabled performers. Directed by Adina Tal, this production from the Nalagaat Theater of Tel Aviv features a cast whose members are all, to some degree, deaf and blind. And the show has them speak of (through signed and supertitled interpretations) and act out their dreams of a life in which they can see and hear.

The forms that these fantasies take evoke silent movies, of both the sentimental and comic variety, and vaudeville routines. In other words, their interior lives have been translated into a language of spectacle that a sighted and hearing audience is familiar with. For the most part they’re reaching out to us, rather than asking us to come to them.

While some of the company members are indeed adept in conventional performance modes (a woman who plays the piano, a stilt walker, a pair of roughhouse comedians with crackerjack timing), much of what they do doesn’t take us beyond the threshold of their interior worlds. To begin to make that journey you need to watch how they communicate by touch with one another, a connection that exudes an autonomous strength, eloquence and physical grace.

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Graceful is hardly the word for the acting styles on display in Radiohole’s “Inflatable Frankenstein” and Half Straddle’s “Seagull (Thinking of you),” nor would their performances consider it a compliment if they were thus described. These riffs on classics by Mary Shelley and Anton Chekhov, part of the Performance Space 122’s Coil Festival of experimental theater, are both by Brooklyn troupes with their own defiantly scrawled signatures.

Radiohole and Tina Satter’s Half Straddle belong to a generation of avant-garde theater artists who are both descended and consciously different from impenetrably polished deconstructionists like the Wooster Group and phantasmagoria-spinning head trippers like Richard Foreman’s Ontological-Hysteric Theater. These younger companies embrace awkwardness and even amateurishness to emphasize the separation between performers and performance.

The beer-swigging members of Radiohole are like giddy overgrown students, goofily stumbling over their own insights. (In the case of “Inflatable Frankenstein,” which features some gasp-inducing technological effects, this involves some astute, self-sabotaging observations about birthing a monster, a play and standard-issue children.)

For Ms. Satter’s “Seagull,” which dissolves the barriers between Chekhov’s characters and the actresses who play them, familiar lines of dialogue are redistributed among the cast and then recited with varying degrees of proficiency. The show can feel too precious by half, but it has the virtue of making us rehear and rethink well-worn passages from a much-studied, much-performed play.

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In contrast Tim Crouch, the writer and sole performer of “I, Malvolio,” brought to New York by the New Victory Theater, inhabits his character with the seamlessness and fluency we expect from British actors in Shakespeare. Yet in its way his performance — an embodiment of the puritanical, ill-used steward from Shakespeare’s “Twelfth Night” — is almost as challenging as those in “Ganesh.”

Greeting us in soiled long johns, with a “kick me” sign on his back, this Malvolio recaps the plot of “Twelfth Night,” with special emphasis on the humiliations he is subjected to, as he chides us for enjoying the vision of one man’s abasement. He enlists audience members to boot him in the rear, to tie his shoes and even to assist him in his own hanging.

“Is this the kind of thing you find funny?” he asks in exasperation. He’s preaching to us, and he’s the kind of preacher we’d like to shower with spitballs. Yet even dour, pompous preachers and teachers can make valid points. Mr. Crouch’s Malvolio finally walks out on his audience, leaving it to wonder whether to stay in or leave their seats.

Being denied the customary closure of a curtain call sure feels frustrating. But that omission, in its silence, speaks loudly on behalf of all these recent shows that refuse to let us take actors — and our relationship with them — for granted.