When is it required to use 's in phrases like below (examples taken from Wikipedia)?
Are there any rules for eliding Saxon genitive?
How does the situation change if we have something instead of somebody?
I wouldn't think of it as "eliding" anything: there are two different constructions:
possessive + noun
modifying-noun + noun
The first is mostly limited to animate possessors, and denotes something belonging to or specifically associated with the possessor, whereas the second is not so limited, and denotes a less specific association.
In the cases you have given, either is possible*, with little or no difference in meaning. But sometimes one is impossible, or there is a difference in meaning. So
007 theme
Means a theme associated with the idea or the person 007, whereas
007's theme
is specifically thinking of 007 as a designation of a person, and specifying a theme associated with that person. Similarly
James Bond theme
is ambiguous as to whether it means a theme specifically associated with the character of Bond, or more generally associated with the phenomenon (or brand) James Bond.
*At first I didn't think "007's theme" was possible, until I remembered that "007" can refer to the person.
