This is "A Little Peace and Quiet" from The Twilight Zone.
While doing a little gardening (to the tune of her neighbor’s chainsaw), Penny digs up a necklace with a watch on it. That afternoon after a hectic trip to the grocery store, spilled milk, and an idiot husband, she clasps the watch and screams, “SHUT UP!” To her shock and awe, there is immediate ...
Who? (1958) is a science fiction novel by American writer Algis Budrys, set during the Cold War.
Plot according to wikipedia:
An explosion resulting from an experiment gone awry rocks an Allied research facility near the border with the Soviet Bloc. A Soviet team abducts Dr. Lucas Martino, a leading Allied physicist in charge of a secret, high-priority ...
This is probably "Thunder and Roses" by Theodore Sturgeon. From this Reader's Guide to the story:
Pete Mawser and Sonny are survivors of one-half of a nuclear war, stuck on a military base, both plagued by thoughts of suicide. They discover a formerly hidden door that has unlocked due to the high-level of radiation. They get spooked and leave. Starr ...
"Something to Say", a novelette by John Berryman, also the (unaccepted) answer to this other question; published in Analog Science Fiction -> Science Fact, August 1966, reprinted in the 1968 anthology Analog 6 edited by John W. Campbell.
The viewpoint character is an American non-violent pacifist
I shrugged again. "I'm neutral," I said. "If that means ...
Psychic Warrior by Bob Mayer aka Robert Doherty. Read it a few times, almost certain this is the one you are looking for.
It's set in 1981 and opens with military psychics attempting to "remove-view" Russian sites. After it doesn't work, Project Grill Flame is shuttered, at least officially. Off the books, it was renamed Bright Gate, and is dedicated to ...
You're looking for Who? by Algis Budrys. Published in 1958, but taking place in an alternate 1970's. The soviets abduct a scientist; Lucas Martino. Several months later, he is returned with a metal skull and mechanical arm.
His biological hand has his fingerprints, but that may have been transplanted. The thrust of the the novel is determining who he is.
This sounds like Star Fire by Ingo Swann published in 1978.
Your plot points match my recollection of the story. but I don't have access to a copy right now to confirm.
From memory Star Fire has
a protagonist who becomes a super psychic
he discovers psychic weapons programs being run by the USSR/USA
he intervenes to shut down those programs?
a one point ...
Possibly James P. Hogan's Voyage from Yesteryear? The Wikipedia article on it may seem familiar:
The story opens early in the 21st century, as an automated space probe
is being prepared for a mission to explore habitable exoplanets in the
Alpha Centauri system. However, Earth appears destined for a global
war which the probe designers fear that ...
Could this be "Tool of the Trade" by Joe Haldeman?
The main character invents some device for controlling minds. I don't recall there being a second character in the USSR, but the CIA and KGB are involved somehow.
Parts of this remind me of Richard Doherty's Psychic Warrior series. There's the cold war, psychics who specialize in remote viewing, and some horrific descriptions of the psychic attacks. However, I don't have access to the book at the moment, so I can't confirm details further than what's in the Goodreads blurb.
In 1981 psychics were secretly gathered ...
Possibly the series of six short stories by Clarke which were published collectively as 'Venture to the Moon'
"The Starting Line" tells of the launch of the first lunar expedition jointly by British, American and Russian rockets which have been assembled in Earth orbit. The plan is for all three ships to leave Earth orbit and land ...