The use of warned would be more appropriate, in my opinion. Although ordered is considered stronger, if you will, it is usually connected to more authoritative figures such as military commanders or police. The police officer ordered the crowd to stand back. The cops ordered the men to get out of the car. The platoon sergeant ordered the medics to give first aid to the wounded child. My commander ordered me to report to him at 1300 hours. However, if you are trying to get the point across that the archaeologists did all they could to prevent the children from touching anything, you could add an adverb in front of the verb, such as emphatically warned, expressly warned, or repeatedly warned. The archaeologists expressly warned the children against touching anything. The archaeologists repeatedly told the children to not touch anything. Hope that helps!

Actually you can both use it, but the difference between the two words is "Order" word is much stronger than warn. Order word is like making a rule and its a mandatory to do it. while the.. "Warn" word its not that strong than the order word. Warn word its just like a suggestion so you have a choice to follow it or not, but the point it is stating that there will be possible consequence if your not going to follow it.

Neither A or B is correct in this situation. The archaeologist ASKED if any decisive steps ahd been taken to save the situation. Otherwise: Use "warn" when you warn someone. Use "order" when you order someone. Look both word up in a dictionary.

Both work fine, though 'ordered' is quite authoritative, whereas 'warned' is more friendlier.