In the more recent Star Treks (Enterprise, DS9 and Voyager), the same actors have been used to portray several characters. An example is Jeffrey Alan Combs, who played Weyoun and Brunt in DS9, Shran in Enterprise and Penk in Voyager, among many others.
All of these characters, obviously, look similar, and so my question is as follows: is there any in-universe explanation for the similarities between the characters?
Whilst there isn't any specific in-universe answer to this, I thought I'd provide a mixing of "real world" and ST universe that could provide an answer.
Real World
Within the human genome, there is a limit to the number of variations of our genes. Given that only a portion of those genes provide for physical characteristics, the odds on duplication are even higher. You can see this in day to day life with celebrity lookalikes (although admittedly some of the lookalikes are tenuous at best).
Given this limitation, as the number of members of the species increase (e.g. due to planetary migration), the likelihood of people who look alike will increase.
This BBC article discusses the likelihood of having doppelgangers around the world.
So that provides a possible explanation for intra-species lookalikes. But what about inter-species lookalikes?
In Universe
For that, we need to turn to the ST:TNG episode: The Chase with the above in mind. In this episode, factions from several species attempt to chase down a weapon hidden within the genetic code of species from all over the quadrant.
In the end
They discover that the code produces a hologram of a genetic progenitor. Whose race sought to create new races in their image.
The script for this episode can be found here. But the relevant section is quoted below:
Our scientists seeded the primordial oceans of many worlds, where life was in its infancy. These seed codes directed your evolution toward a physical form resembling ours -- this body you see before you.
So, since all the races share this in common, it would not be a large stretch to extend the likelihood of doppelgangers to all humanoid species, rather than just humans.
As a fun-fact, its worth mentioning that the hologram in The Chase is played by Salome Jens. If she looks familiar, that's because she also plays the main Founder in ST:DS9
You're asking for an in-universe explanation for something that doesn't exist in-universe.
For instance, Marc Alaimo plays several Trek characters. In-universe, nobody ever asks Gul Dukat if he's aware of his striking resemblance to a Romulan that Picard met once. In-universe, the two bear no resemblance to each other.
Out-of-universe, they could have used a different actor for each and every character in all five series (there is plenty of talent out there), but in most cases it's a better use of your time to ring up an actor whose work you've liked in the past.
There's a perfectly reasonable explanation for this, and there's an actual economy surrounding this reason in our society today. That reason is: sometimes people just look alike.
Any similarities between characters due to the same actor being utilized can easily be rationalized in-universe by concluding that either A) they're related somehow or B) pure chance. After all, we have actual people being paid to look like celebrities in our own society, not to mention all of the other instances of awkward social interactions people have when they approach someone who looks like someone they know, but it turns out to be a complete stranger.
There are a few instances where there is an explanation. In Star Trek VI, Michael Dorn plays Colonel Worf, not to be confused with his 24th century counterpart. While never stated onscreen, Memory Alpha confirms that the writers intended for Colonel Worf to Next-gen Worf's grandfather. The likeness between the two characters (most notably in their voice) is therefore explained by familial connection.
The same is true for Tasha Yar and her half-Romulan daughter Sela, both played by Denise Crosby.
Also, bit of a cheeky afterthought, but Jonathan Frakes plays both William Riker and Thomas Riker, who are transporter duplicates. My personal pet hypothesis is that characters played by the same actor are in-universe duplicates of each other due to time travel or some other techno-nonsense. But obviously that struggles to explain characters of different species.
In all of the cases you mentioned, the same actor played members of completely different species, so there's no in-Universe reason for the similarities other than being humanoid and some resemblance that might be expected after all.
Why do you think that the characters "actually" look like the actors who portray them? What is the logical justification for believing that?
Every work of fiction needs a frame story to explain how the information about the events in the story came to be known. Especially stories set in the future that necessitate the information travelling back in time to the era when the stories are written or the movies and TV shows produced.
But only a tiny minority of stories have official frame stories. For the vast majority of stories without official frame stories fans can only imagine the different types of possible frame stories and wonder which ones apply to which stories.
So in the case of Star Trek one extreme type of frame story would have actual ship board record tapes from various missions travelling back in time and being edited into hour-long television episodes and a few movies. In such a frame story the visual look of Star Trek would be very accurate.
In a very opposite type of frame story a time traveler could have been the babysitter for little Gene Roddenberry and told him stories from space travel history. And decades later Gene Roddenberry makes a TV series based on the almost forgotten stories told him as a child. In such a frame story only a small part of the plots of various episodes would be true and the visual aspects would be due to countless 20th century decisions as the production staff hired actors and made props, sets, and costumes and thus would be very different from the true appearances of people, places, objects, ships, etc., etc.
And since there is no official Star Trek frame story and probably never will be one, no fan can be certain that any of the characters look like any of the actors who portray them. Asking questions about the appearances of people, technology, ships, etc. in Star Trek is making the assumption that the frame story of Star Trek enables the accurate depiction of the looks of people, places, and things. And that is a very unsafe assumption to make.
