TL;DR: (as question was updated)
Is there any explanation (in- or out-of-univsrse) on why Gerald was able to imitate sound effects only and how he was so good at it?
Out of universe, and going back to 1950, no, there does not seem to be an explanation for him.
In-universe, unless there was an opportunity to expand and explain this in the 2005 remake that you missed (because I haven't watched any of them), then no.
Gerald McBoing-Boing is a Dr. Seuss script that was made into a record for release in 1950.
Dr. Seuss's script consisted almost entirely of voice-overs and sound effects
With the success of the record, it became an animation (but not in Dr. Seuss style) from studio UPA which incidentally would become known for the Mr. Magoo animations, which is why the animation style and look is similar.
Gerald McBoing-Boing later became a book in 1952 after the success of the animation.
Dr Seuss' artwork has been described as surrealist, and as such his subjects and stories are rarely relatable to the real world, but do take inspiration from it (often from where he lived).
the 2005 TV series was a remake, hoping to kick start a revival of the character which ultimately failed.
Note: In both the original artwork, and then the subsequent book artwork, he is depicted as a human boy, so he is unlikely to be thought of as anything but that, as likely intended by the author.
So, based on the above, and that the OP's question is about a remake, and given the origins of the original, it is very unlikely that the character would be explained in a satisfactory way for the OP. Gerald is simply a little human boy that started exhibiting this strange feature at age 2.
Whilst some of the characters might be human, the Sam-I-Am or The Lorax creatures, for example, are never explained.
1952 art, 1953 Dr Seuss art, 2005 remake
Recording, the origin of Gerald:
Comic book references:
All indicate that he is simply a human boy that is suddenly affected by this:
"UPA presents"; Illustrated script of a recording originally by Dr. Seuss. The Toon Treasury reprint credits the art to P.D. Eastman. Here's the script from the first two panels: "This is the story of Gerald McCloy... ...and the strange thing that happened to that little boy."