The new show “Dead as a Dodo” opens with the word “Bone!” Followed by “Death! Death! Death!” This isn’t the kind of dialogue you’d expect from something advertised for ages 7 and up, but no matter how young its audience members are, the company Wakka Wakka never underestimates their intelligence and willingness to engage in serious matters.

This sort of experimentation is par for the course at the annual Under the Radar festival, now on stages across New York City. It’s just that “Dead as a Dodo,” one of 33 works in the festival, does it better. From a formal perspective, it is among the most ceaselessly inventive pieces of theater I have seen in the past year.

Written and directed by Gwendolyn Warnock and Kirjan Waage with help from the ensemble, the piece follows the adventures of a long-dead boy and his best friend, a dodo — a flightless bird extinct since the 17th century — in a spooky underworld. Both of them have been reduced to skeletons at first, and the action starts off with the boy looking for bones to replace his missing ones.

The show, at the Baruch Performing Arts Center through Feb. 9, is as morbidly poetic as “The Nightmare Before Christmas.” It immerses the audience in a fantastical universe — at one point, plunging underneath the fiery river Styx — thanks to outlandishly inventive puppetry (Waage designed the figures), projections (by Erato Tzavara), lighting (by Daphne Agosin) and audio (sound and original music by Thor Gunnar Thorvaldsson).

The hell we are in may be of our own making: “Dead as a Dodo” concludes Wakka Wakka’s eco-minded trilogy, following “Animal R.I.O.T.” and “The Immortal Jellyfish Girl,” and is concerned with the evolution of the natural and human worlds. The bigger story here is concerned with new beginnings, and it is told gorgeously.

Rejecting the naturalism that tends to dominate mainstream American theater is among Under the Radar’s main tenets. The festival takes form seriously, and all the shows I saw in this year’s cohort pushed direction to the forefront, even in the docu-play “SpaceBridge,” which concluded its short run this weekend at La MaMa, in association with En Garde Arts and Visual Echo.

Conceived and directed by Irina Kruzhilina, “SpaceBridge” follows the lives of a group of actual young Russian refugees in present-day New York City and, to a lesser extent, some of the American kids they meet here. The children’s stories emerged in theater workshops they took part in, and they now retell them under the benevolent eye of Samantha Smith (played by Ellen Lauren), a real-life American peace activist who died at 13 in a 1985 plane crash. She is imagined here as a gentle adult.

“SpaceBridge” could have coasted on its inherent emotional power — most of the Russian children in the show are still waiting to hear about their asylum requests — but Kruzhilina has made a very theatrical work. She varies dramatic formats, from re-enactments to vaudevillian skits; mines the full depth of the La MaMa stage; and inventively integrates props like old-fashioned suitcases. There is a dynamism to the storytelling that never lets up, especially when the show pointedly touches on down-and-dirty political maneuverings.

At a further remove — literally so — from such earthly concerns is “The 7th Voyage of Egon Tichy [Redux],” which is at New York Theater Workshop’s Fourth Street Theater through Jan. 26.

Based on a story by the science-fiction writer Stanislaw Lem, the show — created by the director Jonathan Levin, the playwright Josh Luxenberg and the performer Joshua William Gelb — takes place on a spaceship where a lone traveler finds himself in a spatiotemporal pickle. When an earlier version was streamed live in July 2020, Gelb interacted with multiple versions of himself thanks to simultaneous video editing (that version is still available on YouTube). Amazingly that is still the case in the new iteration, in which we can watch Gelb in person and on the two screens that flank his tiny performing area. Much of the show is spent wondering which of the Gelbs onscreen is live and which was prerecorded then mixed into the proceedings.

Unfortunately the storytelling can’t keep up with the gimmickry, and “Egon Tichy” becomes tediously repetitive. This is made worse by the padded running time — the show has grown from 35 minutes to almost an hour. Did the creative team think they needed that to justify a live version for paying customers?

The last two works I saw also struggled with their relatively economical lengths.

Following a residency in Portugal, Robert Schenkkan — best known for his Lyndon B. Johnson shows “All the Way” and “The Great Society” — wrote a short satire, “Old Cock” (at 59E59 Theaters through Jan. 19) for the Porto company Mala Voadora and its artistic director, Jorge Andrade.

Andrade is alone onstage, in a resplendent feathery costume, as the fabulously combed rooster of Barcelos, a fowl that is Portugal’s folk emblem. The monologue turns into a dialogue when António de Oliveira Salazar (also Andrade), who ruled Portugal with a dictator’s fist until 1968, turns up on a video screen. The rooster confronts him about the manipulation of national symbols for autocratic purposes — which sounds tragically relevant, but the attempts at humor fall flat and the attempts at political thrusts feel blunted.

Geopolitics also play a major role in Amir Reza Koohestani’s “Blind Runner.” The play, which is presented by St. Ann’s Warehouse through Jan. 24, with Waterwell and the arts-and-education organization Nimruz, aims to be a suspenseful thriller about a blind Iranian woman trying to run the length of the tunnel between France and Britain at night before trains resume their service.

But this political statement takes up just the last few minutes of the show. The bulk of it consists of stilted conversations between the runner’s eventual guide (Mohammad Reza Hosseinzadeh) and his imprisoned wife (Ainaz Azarhoush) during his weekly visits to her. Koohestani is much better as a director than a writer, and he stages these static interactions in a sleek, austerely elegant manner — Éric Soyer’s lighting carves out his minimalist set with the suggestive power of a German Expressionist movie.

Of course, any festival will be uneven. Surefire bets don’t exist, but shows that look to be worth a visit include a staging of Shuji Terayama’s “Duke Bluebeard’s Castle” (Jan. 15-18 at Japan Society) that allows us a glimpse into experimental Japanese theater. Odds are good that at least it won’t be like much else in town.

Under the Radar
The festival runs through Jan. 19, but some productions have longer runs; utrfest.org.