Can I use images with a "noncommercial use only" license (such as CC-BY-NC) in my slides, both for teaching and conference talks?
I'd bet it's probably fine, but there's no way to get a definitive answer without asking the copyright holder (this is one of the weaknesses with the noncommercial Creative Commons licenses). The Creative Commons definition of commercial use is use that is "primarily intended for or directed towards commercial advantage or monetary compensation". Most teaching and conference talks seem pretty clearly noncommercial to me by this standard. But what if someone argues that you're only doing that teaching to earn money? Does the mere fact that you are using this material to help you do your paid job transform it into commercial use, or can you argue that in fact your use was not motivated primarily by earning money? What if you're getting paid an honorarium to give a talk - does that make it even more of a commercial activity? You could end up in all sorts of debates about what the "primary intentions" are, with many borderline cases, and there's no objective way to resolve the disagreement.
The Creative Commons organization does not attempt to settle these issues, but does note that "not all educational uses are necessarily NonCommercial uses, so your use of an NC license may preclude use of your work in some educational contexts". There seems to be no official guidance as to what this is intended to cover. Maybe it is limited to cases such as selling teaching materials, or maybe it is much broader.
In practice, I imagine most people using a noncommercial license would not object to these uses. There is a study of what users have in mind when choosing such a license, which doesn't directly address your issues but may shed light on them. However, it's worth noting that people have in fact had nontrivial disputes over what constitutes noncommercial use, with at least one court decision that disagrees with what I would have predicted.
I can't really imagine anyone would sue you over ordinary teaching or conference talks. The worst plausible scenario is probably offending the copyright holder (and being asked to remove the image), not getting sued. That could be a risk worth taking if you believe that these uses should be considered noncommercial.
Of course I'm not a lawyer or an expert in Creative Commons licenses, and I don't know the real risks, so you should take this whole answer with a grain of salt.