If in the phrase was used for and,

when “a” does not mean and although that is a decent guess.

When puberty comes knocking

The a- is known as A-prefixing and is a feature of some dialects.

When puberty comes knocking

You essentially can remove the “a-” from knocking to get the intended meaning When puberty comes knocking In this case it gives it a less formal colloquial feel.

to be of and to have express two different ideas although in some contexts they may seem similar

• to have is a verb describing possession of the subject.

• To be of describes a property of the subject.

“Degree” is describing the quality of the pain. We would not think of a degree as something the pain has/possesses.

Thus,

The pain is of a degree that calls for morphine

would be understood.

An unnatural pain has a degree that will call

for morphine.

If you want a word to say “is”, you

could say: The pain has an intensity that calls

for constant morphine.