utility vs command
 

Can anyone tell me the difference between a command and a utility in a Linux system?

How are they each related to a program? Is there any formal definition for them that distinguishes them?

There isn't one, really. A 'command' may be considered a utility, really...such as "ls" is a command to do a directory listing, and can also be considered the UTILITY that you run to find out what files are in a directory. That's like asking, "what's the difference between a car and an vehicle?"
Depends on what program you're talking about, in what context.
No.

Also, you've been using Linux for four years now....and this sounds very much like a homework question.

you may say program, utility and command are more or less the same thing (or synonyms).