I haven’t even the strength to swing vs. I haven’t even got the strength to swing

Solution 1:

There are two issues here, that one shouldn't confound.

First, there is the question of using got or not whenever one uses the verb have. Do you say I have a book or I've got a book? Answers depend on where and by whom you are taught English, but the meaning of those two sentences is the same.

The second point is the placement of even. To make a fair comparison between the Original sentence, and a version with got added, I would compare:

I haven’t even the strength to swing...
I haven't got even the strength to swing...

These two sentences mean the same, even modifies the strength to swing all the way around.

With even in a different position, you get

I don't even have the strength to swing...
I haven't even got the strength to swing...

This time, even modifies the verb have.

Although very similar in meaning, there is certainly some difference in nuance between I don't even have the strength and I don't have even the strength/I haven't even the strength.