As for parodies, there exists The Star Trek Man;

I am the Star Trek Man,
I come from down your way,
What can you play ?

I can play [name of character]

Mr Spock:
It's life Jim, but not as we know it
not-as-we-know-it, not-as-we-know-it.
It's life Jim, but not as we know it
not as we know it.

Dr. McCoy:
It's worse than that he's dead Jim
dead Jim, dead Jim,
It's worse than that he's dead Jim
dead Jim, dead.

Lt. Uhura:
Hailing channel open sir
open sir, open sir.
Hailing channel open sir
open sir, open.

Mr Scott:
The engines canna take it Cap'n,
Take it Cap'n, take it Cap'n.
The engines canna take it Cap'n,
Take it Cap'n, take it.

Security Man (or red-shirt):
AAAAAAAAAAAAAAHHHHHHHHHHHHHHH-ck!

(plus others)

And then it got recorded!, but differently, which lead to a court case. I personally believe this song grew up all over the UK (at least) in different places simultaneously. I know I created the Spock verse in variant above. I hastily add I wasn't involved in the court case. But I know some people who were.

AndyG