Each row comprises synonyms except "put out the light" can also mean turn off a non-electric light whereas the other two would generally be used for lights operated by electric switches. To "put off" can also mean to discourage - "his unhelpful attitude put me off offering him any help.

turn out a light > X Its either turn on or off the light put out the light / put out the campfire > ok turn off a light > ok > turn the switch off go off = blow up= to explode >the heat caused the bomb to go off/blow up/explode. ( go off here means it exploded) But , go off is used only for things like gun , bombs or similar things that are inclined to cause an explosion / or to fire You cant say " the tanker went off , but you can say " the tanker exploded/blew up" The gun went off accidentally ( here it means it fired) put off / delay / postpone = quite similar in meaning ,but there are differenes in usage to put off > to do something at a later time . Could you put the meeting off till next year ? > here youasked him to change the time) to delay > to make something done not fast . Could you delay the meeting till next year? > here you are asking him to " slow down" the approach of the meeting Postpone > to change the date of something to a later date to replace the one that is scheduled > Could you postpone the meeting because the date set next week is not suitable for me ? > here you replace a set date with a later date