Not quite odd, but my all-time favorite cameo was Jack Riley in the episode of “ALF” where Bill Daily was first playing a psychiatrist.
Similarly, Suzanne Pleshette in the Newhart finale was a great one.
The weirdest, though, are the number of times that Stephen Hawking voices himself. Given how busy Dr. Hawking is & how easy it would be for TV programs to get an exact match, it always surprises me when the credits show that he was playing himself.
The currently in theaters Passengers has one (though maybe technically not as he is listed in the credits). Can’t see how it could spoil anything but since it is still recent:
[spoiler]At the end of the movie when the ship arrives at its destination the crew is shown coming out of hibernation into the main area. Among them is Andy Garcia.
He has no line, he’s on screen for maybe three seconds. The role had no impact on the movie.
For the life of me I can’t figure out why he’s there unless they’d filmed something much more involved for that part of the movie and then it all got cut.[/spoiler]
Perhaps not odd but prescient: Arnold Schwarzenegger had a cameo in Dave.
Getting a physical likeness could be a bit difficult, though the advances shown in Rogue One are promising. But his lines must be a relative doddle to do: the scriptwriters just feed the lines into his voice computer and he just has to activate it at the right time (granted that’s no small feat for him). Perfect delivery every time.
Stephen Hawking is the world’s most famous fanboy. He appears or has the voice used in so many shows because he wants to. He has asked to appear in various shows. He knows he can appear in anything he wants now.
Just don’t ask him about black holes.
That’s his real voice, you know. 
Daniel Craig as the storm trooper that Rey uses the Jedi mind trick on to get loose from the comfy chair.
I think it was more than a cameo but in the Star Trek movie with Christopher Lloyd as a Klingon there was also John Larroquette as a Klingon. I remember reading that at the time there were a number of big names wanting to do bit parts as hard to recognize (due to makeup) characters.
Yes, albeit from a voice synthesizer. 
John Tesh played a Klingon in a Star Trek episode, I think it was the Next Generation
What I was gonna say. It’s a fun film.
Says he was named in his second appearance.
His IMDB list seems to show a much bigger career than you are aware of.
Bumped.
The future King of Jordan was in an episode of Star Trek: Voyager:
http://memory-alpha.wikia.com/wiki/Abdullah_bin_al-HusseinSteve Martin’s, “The Man With Two Brains,” has an odd cameo by Merv Griffin; I dunno why, it’s not all that funny or interesting.
It amused me.
One of the best scenes! I love how Merv rants about not having the ability to lurk because of his fame. 
Lurk. Funny word.
Senator Alphonse D’Amato in “Devil’s Advocate”. Also Victor Mature in “Head”. (The surreal Monkees film.) The latter also had Annette Funicello as a character named “Minnie”.
Oh, and it’s on YouTube
Billy Ray Cyrus in Mulholland Drive.
Groucho Marx in Will Success Spoil Rock Hunter (1957).
Noel Coward, Marlene Dietrich and Tony Curtis in Paris When it Sizzles (1964).
Natalie Wood in *The Candidate *(1972), which also boasts a cast full of contemporary politicians, newsmen and Groucho Marx.
Yul Brynner in drag, singing seductively to Roman Polanski at a bar in The Magic Christian (1969). Also with brief bits from Laurence Harvey (stripping to Hamlet) Raquel Welch, Christopher Lee, John Cleese, Graham Chapman, Richard Attenborough and others.
Senator Everett Dirksen of Ill. in The Monitors (1969), among others.
John Hurt in Spaceballs (1987), proving himself the finest chestbusting thespian the silver screen has ever seen.
Digitally reanimated Laurence Olivier in Sky Captain and the World of Tomorrow (2004).
Digitally de-aged Alice Cooper in Dark Shadows (2012).
In the movie California Suite, Maggie Smith plays an actress up for an Oscar. At one point, they show a clip of her nominated performance set in an airplane.
The pilot of the airplane in the movie-within-a-movie is James Coburn. He even has a couple of lines, but was uncredited.