Could Azazel jump into an insect or a microbe?

That's exactly what I was wondering. If so then you're screwed because you'd have to really choose your battleground, VERY carefully. Maybe a sealed bio containment lab, room, etc. In the woods you have all sorts of critters that are about such as, ants, mice, rats, toads, birds, bees, flies, mosquitoes, etc.

So no matter what you did with a little luck there's always some life form around to jump into. But on top of that, the bigger question is did Azazel have the power of summoning? Meaning being able to call a life form to him, to get it to come to him where ever he was at. This is never explained in the movie but if by chance he did, then you'd really be screwed! Just a thought.

He’s a spirit so he probably never dies regardless of livings or story.

But to answer your question he probably can as you can see that animals have spirits just as anything else.

The ‘only way to be sure’ is to blast his current host into space.

Insect or arachnid certainly so.