Non magical elemental damage in Skyrim

Solution 1:

Poison is not considered magical, however Poison Damage Reduction does exist such as the Bosmer's Special Ability

Resist Disease and Poison:

Your Bosmer blood gives you 50% resistance to poison and disease

To answer the other half of your question, no there are no non-magical sources of fire/frost/lightning damage. This means that magical resistance will always work, as will fire/frost/lightning resistance respectively

It's worth noting that there are traps that do one of those kinds of damage, but it's considered magic damage (Ex: Flamethrower in dungeons). And your damage reduction will work on said traps.

Sources:

• IGN's Race Comparison
• UESP's trap mechanics/information

Solution 2:

According to the description for the Resist Magic effect:

Resist Magic is capped at 85%, this includes all forms of elemental and dragon breath attacks.

On this page, it is also noted that Resist Magic is more versatile than simple elemental resistances:

Gaining a resistance to magic can negate a percentage of all incoming spells. It is more versatile than elemental resistance as it covers all kinds of magical damage instead of just fire, frost, or shock individually.

Thus, Resist Magic covers all sources of elemental damage, including damage on elemental weapons, such as the Aegisbane.

Solution 3:

Looking through the Creation Kit, it appears the effect from the Staff of Magnus does not have a resist value listed. I'm a bit skeptical that I'm not missing something though, since the UESP do not mention that it is special in not being affected by resistance.

Similarly, with the exception of the "Fake Lightning Bolt" effect, the Skull of Corruption has no resistances listed for any of its damaging effects.

It looks like some elemental traps have a resistance listed and some don't. Someone more familiar with the CK than I might be able to tell you where some examples are actually located, the best I can tell is what cell they are located in (e.g. Saarthal02).