How can we objectively evaluate the strength of a non deductive argument? ... how does one objectively analyze the strength/weakness of a non deductive argument, or what it even means for an argument to be strong or weak?
I'm not sure where the assumption that an evaluation would be objective comes from.
An abductive conclusion needs to at least be consistent with the premises/observations. A conclusion inconsistent with the premises/observations can be ruled out.
Beyond that, assessment of an abductive argument is based on strength of evidence, prior beliefs, credibility and reliability of testimony, coherence, etc. There are many other Q&As on this site about those.
Abduction is "everyday reasoning."