If you say

ça y ressemble de près

It means that if you get very close from the object, it will be very similar to what you are talking about (here, a hunting rifle). You may say that for an imitation for instance.

If you say

ça y ressemble de loin

It means you have to be far from the object to be able to say “it is the same” (here, it is a hunting rifle).
You will use this to point the fact that if you get closer, you easily see a difference.

So here

Je n’avais rien qui ressemble de près ou de loin à une arme de chasse.

Means you have neither a hunting rifle, nor something that could be used as a hunting rifle.

de près ou de loin is a french expression, that mean

In any manner

approximately.

This phrase mean :

I had nothing resembling in any manner to an hunting weapon.

“De près ou de loin” is a French expression meaning “considering every possibilities”. It emphasis on the fact that nothing looked like what was looked for. Even considering a close inspection AND a macro-vision.

However, your sentence is incorrect, verb tenses should be linked. The correct sentence would be : “Je n’avais rien qui ressemblât de près ou de loin à une arme de chasse.”

Literally, your sentence means : “I had nothing that looked like a hunting weapon”.

A simple search on Google with this words returns this definition in French

What might be the meaning of this entire phrase?

Idiomatically it would be “I had nothing that looked like a hunting rifle from any angle” or perhaps “I had nothing that looked like a hunting rifle from any point of view.”