How do I know which damage type monsters inflict?

The only true way to find this out is testing. You could easily do this on normal.

You should do multiple runs with 0 Resist All to get the control information. I would say a sample size of at least 10 kills. Average the damage from each fist attack (or whichever attack of his you want to figure out) across all runs and that is your control figure.

Once you have the control, you can start introducing variables like each separate Resist stat. I would start with Physical Resist, preferably a very high amount, so you can more easily see the impact it has without the difference falling within the margin of error. Do the same amount of runs and average the damage once again. Technically, if the attack indeed is Physical, you should see a reduction very similar to the amount of reduction your Resist stat is giving you. The more runs you do and the larger the sample size is, the more accurate this will be and the closer the actual reduction you see will be to the amount the stat says it will reduce by in the character sheet.

You will most likely have to spend gold on the proper gear to do this, but it is the way people have found out many of the games mechanics and nuances. FRAPS or some other form of recording is also a good idea so you don't have to write things down during the fight.

This may not be the easy answer you wanted, but it is the scientific method, and it's how humans have been figuring things out for years! Especially theorycrafters in video games!

I have come across this question while trying to find the answer to the same question.. I have subsequently found what I was looking and anyone else with the same question here:

http://www.ctrustnetwork.com/c515p1/gaming/diablo-3/bestiary.html

Maybe this will save the next poor sod some time.