Martial Law ... it's the kind of thing you hope never happens. it is more likely to occur 'locally' rather than nationally. e.g. a specific city that has a major rhreat or disaster.

I would obey all instructions immediately, never be angry or abusive, and NEVER carry anything that could be confused for a weapon. It would be smarter to be in a group, esp. well behaved people. and dont violate curfew hours.

Special military teams could be guarding high priority locations, such as Govt buildings or nuclear facilities. i would avoid these areas completely.

Overseas ... martial law is a risky situation if you are caught up in it. it happened once to me in Africa. i walked away ok, and i remained calm on the outside, but internally I was sweating bullets. you just never know what poorly trained soldiers in 3rd world counties will do. they tried to shake me down for a bribe, but i didnt give them anything. it is risky, very unpredictable.